Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 9, and the edges are: (0,1) (0,8) (0,6) (1,3) (1,9) (2,3) (2,9) (2,4) (3,4) (3,5) (3,7) (3,8) (4,8) (5,7) (5,9) (6,8)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,6,8,4,2,9,5,7,3,1


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 17, and the edges are: (0,7) (0,17) (0,16) (0,1) (0,9) (0,2) (0,15) (0,4) (0,13) (0,8) (0,11) (0,14) (0,10) (1,10) (1,4) (1,17) (1,15) (1,2) (1,14) (1,9) (1,6) (1,12) (1,16) (2,16) (2,8) (2,9) (2,12) (2,13) (2,5) (2,7) (2,6) (3,12) (3,6) (3,16) (3,8) (3,13) (3,7) (4,16) (4,17) (4,7) (4,12) (4,13) (5,8) (5,9) (5,16) (5,13) (5,17) (5,7) (5,15) (6,11) (6,14) (6,12) (6,8) (6,13) (6,17) (6,16) (6,9) (7,10) (7,14) (7,13) (7,17) (7,15) (7,8) (7,9) (8,15) (8,13) (8,9) (8,16) (8,12) (8,17) (9,17) (9,10) (9,15) (9,13) (9,11) (10,13) (10,11) (10,15) (10,14) (11,14) (11,12) (11,13) (11,16) (12,13) (12,16) (13,16) (13,15) (13,14) (13,17) (14,16) (15,16)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,10,14,16,15,13,17,9,11,12,8,6,3,7,5,2,1,4


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 14, and the edges are: (0,9) (0,2) (0,6) (0,1) (0,3) (0,12) (0,14) (0,8) (1,4) (1,13) (1,5) (1,2) (1,14) (1,9) (1,6) (1,11) (2,11) (2,3) (2,6) (2,8) (2,12) (2,13) (2,14) (2,7) (3,14) (3,6) (3,11) (4,14) (4,5) (4,11) (4,6) (5,12) (5,8) (5,10) (6,11) (6,14) (6,12) (6,13) (7,10) (7,11) (7,13) (8,9) (8,11) (8,13) (8,12) (9,10) (9,12) (9,13) (10,13) (11,13) (12,14)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,8,12,14,6,13,11,4,5,1,9,10,7,2,3


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 10, and the edges are: (0,10) (0,2) (0,4) (0,6) (1,4) (1,10) (1,9) (1,8) (1,5) (1,7) (2,4) (2,10) (2,8) (2,5) (3,9) (3,8) (3,6) (3,10) (4,7) (4,9) (4,5) (5,7) (6,7) (7,9) (8,9)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,6,7,9,8,3,10,2,5,4,1


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 17, and the edges are: (0,16) (0,8) (0,1) (0,17) (0,10) (0,3) (0,12) (0,7) (0,5) (1,16) (1,9) (1,4) (1,3) (1,2) (1,13) (1,6) (2,15) (2,8) (2,14) (2,5) (2,11) (3,9) (3,8) (3,13) (3,6) (3,15) (3,11) (3,10) (4,13) (4,14) (4,16) (4,15) (5,10) (5,7) (5,11) (5,16) (5,12) (5,8) (5,14) (5,17) (6,14) (6,9) (6,10) (6,8) (7,17) (7,14) (7,12) (7,9) (7,16) (8,16) (8,12) (8,10) (8,11) (8,9) (9,16) (9,13) (10,14) (10,11) (10,15) (10,13) (11,13) (11,14) (11,12) (11,17) (12,14) (12,16) (13,15) (14,16) (14,17) (15,16)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,5,17,14,16,15,13,11,12,7,9,6,10,3,8,2,1,4


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 9, and the edges are: (0,5) (0,7) (0,1) (0,4) (1,2) (1,9) (1,8) (2,6) (2,5) (2,4) (2,9) (3,8) (3,6) (4,8) (4,9) (5,9) (5,8) (5,7) (5,6) (6,7) (6,9) (8,9)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,4,9,8,3,6,7,5,2,1


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 9, and the edges are: (0,9) (0,2) (0,8) (0,7) (1,4) (1,9) (1,3) (1,2) (1,6) (2,7) (2,6) (2,8) (3,5) (4,8) (5,7) (7,9) (7,8)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,9,7,5,3,1,6,2,8,4


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 19, and the edges are: (0,12) (0,15) (0,10) (0,1) (0,5) (0,8) (0,2) (0,11) (0,13) (0,3) (0,7) (0,19) (0,9) (1,4) (1,6) (1,3) (1,9) (1,11) (1,18) (1,2) (1,13) (1,19) (1,16) (1,14) (1,17) (1,7) (1,15) (2,18) (2,16) (2,14) (2,3) (2,7) (2,8) (2,11) (2,5) (2,6) (2,19) (2,10) (2,15) (3,7) (3,10) (3,12) (3,9) (3,4) (3,16) (3,11) (3,14) (3,8) (4,5) (4,16) (4,10) (4,12) (4,8) (4,11) (4,6) (4,18) (4,7) (4,15) (5,9) (5,16) (5,14) (5,15) (5,13) (5,8) (5,17) (5,19) (5,7) (5,11) (6,16) (6,15) (6,14) (6,10) (6,8) (6,9) (6,17) (6,13) (6,19) (6,12) (7,13) (7,11) (7,17) (7,12) (7,15) (7,10) (8,16) (8,15) (8,14) (8,9) (8,18) (8,13) (8,11) (8,12) (9,15) (9,11) (9,13) (9,18) (9,12) (9,17) (9,19) (10,11) (10,19) (10,14) (10,16) (10,17) (10,12) (10,15) (11,18) (11,17) (11,14) (11,12) (11,15) (11,19) (11,13) (12,17) (12,16) (12,14) (12,15) (12,13) (13,18) (13,17) (13,19) (13,16) (14,15) (14,19) (14,18) (14,16) (14,17) (15,18) (16,18) (16,17) (17,18) (17,19)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,9,19,17,18,16,14,15,12,13,11,10,7,5,8,6,4,3,2,1


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 9, and the edges are: (0,8) (0,6) (0,1) (1,9) (1,7) (2,5) (2,8) (2,7) (3,8) (3,4) (3,5) (4,9) (4,8) (4,7) (5,9) (5,8) (6,7) (7,9)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,1,9,5,3,4,8,2,7,6


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 9, and the edges are: (0,9) (1,7) (1,6) (1,5) (2,3) (2,9) (2,6) (2,4) (3,8) (3,6) (3,5) (3,7) (4,8) (4,9) (4,7) (5,8) (6,7)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,9,4,7,6,2,3,8,5,1


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 9, and the edges are: (0,9) (0,4) (0,6) (0,2) (0,8) (0,7) (1,8) (1,5) (1,3) (1,7) (1,6) (1,4) (2,6) (2,5) (2,4) (2,8) (3,6) (3,4) (3,5) (4,6) (4,9) (5,9) (7,8) (7,9)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,7,9,5,3,4,6,2,8,1


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 9, and the edges are: (0,5) (0,6) (0,9) (0,2) (1,3) (1,6) (1,9) (1,2) (2,9) (2,5) (2,6) (2,3) (3,8) (3,4) (3,7) (3,9) (4,8) (4,9) (4,5) (5,8) (5,9) (5,6) (6,8) (6,7) (7,9) (7,8) (8,9)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,2,3,9,7,8,4,5,6,1


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 13, and the edges are: (0,1) (0,3) (0,4) (0,13) (0,10) (0,11) (0,9) (1,2) (1,13) (1,8) (1,11) (1,4) (1,6) (1,10) (1,7) (1,9) (1,5) (2,11) (2,5) (2,13) (2,3) (2,4) (2,12) (2,6) (3,6) (3,11) (3,5) (3,9) (3,12) (3,10) (3,8) (4,5) (4,7) (4,10) (4,13) (5,9) (5,6) (5,7) (5,8) (6,13) (6,10) (6,7) (7,8) (7,11) (7,12) (8,13) (8,12) (8,10) (8,11) (9,12) (10,11) (10,13) (10,12) (11,12) (12,13)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,9,12,13,10,11,8,7,6,5,4,1,2,3


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 11, and the edges are: (0,11) (0,4) (0,6) (0,7) (0,2) (0,1) (0,5) (0,3) (1,8) (1,4) (1,7) (1,10) (1,3) (1,5) (2,3) (2,11) (3,11) (3,6) (4,5) (4,9) (4,6) (5,10) (6,11) (7,10) (7,8) (8,9) (8,11) (10,11)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,3,6,4,9,8,7,1,5,10,11,2


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 19, and the edges are: (0,11) (0,6) (0,8) (0,5) (0,16) (0,19) (0,15) (0,14) (0,17) (1,3) (1,4) (1,7) (1,2) (1,16) (1,19) (1,18) (1,9) (1,14) (1,17) (1,6) (1,13) (2,5) (2,13) (2,8) (2,11) (2,10) (2,15) (2,6) (2,7) (2,17) (2,3) (2,12) (2,18) (3,14) (3,8) (3,11) (3,17) (3,4) (3,5) (3,9) (3,13) (3,10) (3,18) (4,15) (4,11) (4,8) (4,19) (4,12) (4,14) (4,5) (4,13) (5,17) (5,13) (5,12) (5,18) (5,6) (5,9) (5,15) (5,8) (5,7) (5,19) (5,14) (5,10) (5,16) (6,8) (6,18) (6,16) (6,14) (6,13) (6,15) (7,10) (7,16) (7,9) (7,11) (7,8) (7,18) (7,17) (8,19) (8,15) (8,17) (8,14) (8,12) (8,18) (8,10) (9,16) (9,19) (9,11) (9,15) (9,10) (10,18) (10,12) (10,17) (10,13) (10,14) (10,16) (11,17) (11,14) (11,15) (12,18) (12,19) (13,19) (13,17) (13,15) (13,18) (13,14) (14,18) (14,16) (14,17) (14,15) (15,16) (15,18) (16,18) (16,17) (17,19) (17,18)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,17,18,16,15,14,13,19,12,10,9,11,7,8,6,5,4,3,2,1


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 9, and the edges are: (0,3) (0,2) (0,9) (0,7) (0,1) (1,8) (1,5) (1,2) (2,6) (3,6) (3,4) (3,9) (3,8) (4,6) (4,8) (5,9) (6,9) (6,7)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,7,6,4,8,3,9,5,1,2


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 9, and the edges are: (0,9) (0,5) (0,1) (0,3) (0,6) (1,3) (1,7) (1,2) (1,4) (1,9) (1,6) (1,8) (1,5) (2,7) (2,8) (2,6) (2,9) (3,5) (3,4) (3,7) (3,6) (4,9) (4,6) (5,8) (6,8) (6,9) (7,8) (7,9)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,6,9,7,8,5,3,4,1,2


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 8, and the edges are: (0,1) (0,8) (0,5) (0,6) (0,3) (1,4) (1,8) (1,7) (1,3) (2,8) (2,5) (2,7) (2,6) (2,4) (3,6) (3,8) (4,7) (4,8) (5,6) (6,7) (6,8)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,3,8,6,7,1,4,2,5


Question:
In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (4,2) (0,4) (4,3) (0,1) (0,2) (4,1) (2,3)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 3, and node 3 is not visited, we can then visit node 3.
Therefore, the path can be: 0,1,4,2,3.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 4, and the edges are: (0,4) (1,5) (3,1) (4,2) (3,5) (2,1) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 1. As node 1 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 1,3,5,2,4,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 5, and the edges are: (0,2) (0,1) (4,5) (4,3) (4,2) (5,3) (1,4) (2,5)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 0. As node 0 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 1, and node 1 is not visited, we can then visit node 1.
The path can be: 0,2,5,3,4,1.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 6, and the edges are: (1,4) (3,5) (3,6) (4,5) (0,3) (1,0) (2,4) (6,1)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 2. As node 2 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 3, and node 3 is not visited, we can then visit node 3.
As node 3 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 0, and node 0 is not visited, we can then visit node 0.
The path can be: 2,4,5,3,6,1,0.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 7, and the edges are: (2,3) (5,1) (6,0) (5,3) (7,1) (3,7) (0,5) (6,5) (2,6) (3,4) (1,4) (2,0) (6,4) (1,6)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A: Yes. We can start at node 3. As node 3 is connected with node 4, and node 4 is not visited, we can then visit node 4.
As node 4 is connected with node 6, and node 6 is not visited, we can then visit node 6.
As node 6 is connected with node 2, and node 2 is not visited, we can then visit node 2.
As node 2 is connected with node 0, and node 0 is not visited, we can then visit node 0.
As node 0 is connected with node 5, and node 5 is not visited, we can then visit node 5.
As node 5 is connected with node 1, and node 1 is not visited, we can then visit node 1.
As node 1 is connected with node 7, and node 7 is not visited, we can then visit node 7.
The path can be: 3,4,6,2,0,5,1,7.

In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.
The nodes are numbered from 0 to 17, and the edges are: (0,7) (0,6) (0,9) (0,5) (0,8) (0,17) (0,11) (0,14) (0,12) (0,15) (0,10) (1,16) (1,3) (1,10) (1,5) (1,7) (1,13) (1,12) (1,14) (1,11) (2,9) (2,12) (2,15) (2,14) (2,4) (2,11) (2,10) (2,17) (2,6) (3,16) (3,7) (3,12) (3,17) (3,11) (4,5) (4,16) (4,8) (4,7) (5,11) (5,17) (5,8) (5,16) (5,15) (5,7) (5,10) (6,12) (6,7) (6,17) (6,13) (6,15) (7,17) (7,15) (7,9) (7,16) (7,14) (8,11) (8,14) (8,16) (9,13) (9,16) (9,11) (9,12) (9,10) (10,15) (10,11) (11,12) (11,13) (11,16) (11,15) (12,14) (14,15)
Q: Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges.
A:

Answer: Yes. The path can be: 0,10,11,15,14,12,9,16,8,5,7,17,3,1,13,6,2,4