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 6, and the edges are: (0,6) (0,2) (0,4) (0,1) (1,4) (1,2) (1,6) (1,5) (2,3) (3,6) (3,5) (5,6)
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:

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


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 11, and the edges are: (0,8) (0,5) (0,6) (1,2) (1,7) (1,8) (1,3) (1,11) (2,8) (2,3) (2,10) (3,7) (3,5) (4,5) (4,9) (5,11) (6,8) (7,11) (7,9) (8,9) (9,10) (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: 0,6,8,9,10,11,7,1,2,3,5,4