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def Cell120():
'\n Return the 120-Cell graph.\n\n This is the adjacency graph of the 120-cell. It has 600 vertices and 1200\n edges. For more information, see the :wikipedia:`120-cell`.\n\n EXAMPLES::\n\n sage: # long time, needs sage.rings.number_field\n sage: g = graphs.Cell120()\n ... |
def SuzukiGraph():
'\n Return the Suzuki Graph.\n\n The Suzuki graph has 1782 vertices, and is strongly regular with parameters\n `(1782,416,100,96)`. Known as S.15 in [Hub1975]_.\n\n .. NOTE::\n\n It takes approximately 50 seconds to build this graph. Do not be too\n impatient.\n\n E... |
def HallJankoGraph(from_string=True):
'\n Return the Hall-Janko graph.\n\n For more information on the Hall-Janko graph, see the\n :wikipedia:`Hall-Janko_graph`.\n\n The construction used to generate this graph in Sage is by a 100-point\n permutation representation of the Janko group `J_2`, as desc... |
def Balaban10Cage(embedding=1):
"\n Return the Balaban 10-cage.\n\n The Balaban 10-cage is a 3-regular graph with 70 vertices and 105 edges. See\n the :wikipedia:`Balaban_10-cage`.\n\n The default embedding gives a deeper understanding of the graph's\n automorphism group. It is divided into 4 layer... |
def Balaban11Cage(embedding=1):
"\n Return the Balaban 11-cage.\n\n For more information, see the :wikipedia:`Balaban_11-cage`.\n\n INPUT:\n\n - ``embedding`` -- integer (default: ``1``); three embeddings are available,\n and can be selected by setting ``embedding`` to be 1, 2, or 3\n\n - Th... |
def BidiakisCube():
"\n Return the Bidiakis cube.\n\n For more information, see the :wikipedia:`Bidiakis_cube`.\n\n EXAMPLES:\n\n The Bidiakis cube is a 3-regular graph having 12 vertices and 18 edges. This\n means that each vertex has a degree of 3::\n\n sage: g = graphs.BidiakisCube(); g\n... |
def BiggsSmithGraph(embedding=1):
"\n Return the Biggs-Smith graph.\n\n For more information, see the :wikipedia:`Biggs-Smith_graph`.\n\n INPUT:\n\n - ``embedding`` -- integer (default: ``1``); two embeddings are available,\n and can be selected by setting ``embedding`` to be 1 or 2\n\n EXAMPL... |
def BlanusaFirstSnarkGraph():
'\n Return the first Blanusa Snark Graph.\n\n The Blanusa graphs are two snarks on 18 vertices and 27 edges. For more\n information on them, see the :wikipedia:`Blanusa_snarks`.\n\n .. SEEALSO::\n\n * :meth:`~sage.graphs.graph_generators.GraphGenerators.BlanusaSeco... |
def BlanusaSecondSnarkGraph():
'\n Return the second Blanusa Snark Graph.\n\n The Blanusa graphs are two snarks on 18 vertices and 27 edges. For more\n information on them, see the :wikipedia:`Blanusa_snarks`.\n\n .. SEEALSO::\n\n * :meth:`~sage.graphs.graph_generators.GraphGenerators.BlanusaFi... |
def BrinkmannGraph():
'\n Return the Brinkmann graph.\n\n For more information, see the :wikipedia:`Brinkmann_graph`.\n\n EXAMPLES:\n\n The Brinkmann graph is a 4-regular graph having 21 vertices and 42\n edges. This means that each vertex has degree 4::\n\n sage: G = graphs.BrinkmannGraph()... |
def BrouwerHaemersGraph():
"\n Return the Brouwer-Haemers Graph.\n\n The Brouwer-Haemers is the only strongly regular graph of parameters\n `(81,20,1,6)`. It is build in Sage as the Affine Orthogonal graph\n `VO^-(6,3)`. For more information on this graph, see its `corresponding page\n on Andries B... |
def BuckyBall():
'\n Return the Bucky Ball graph.\n\n This graph is a 3-regular 60-vertex planar graph. Its vertices and edges\n correspond precisely to the carbon atoms and bonds in buckminsterfullerene.\n When embedded on a sphere, its 12 pentagon and 20 hexagon faces are arranged\n exactly as th... |
def GossetGraph():
'\n Return the Gosset graph.\n\n The Gosset graph is the skeleton of the\n :meth:`~sage.geometry.polyhedron.library.Polytopes.Gosset_3_21` polytope. It\n has with 56 vertices and degree 27. For more information, see the\n :wikipedia:`Gosset_graph`.\n\n EXAMPLES::\n\n sa... |
def DoubleStarSnark():
'\n Return the double star snark.\n\n The double star snark is a 3-regular graph on 30 vertices. See the\n :wikipedia:`Double-star_snark`.\n\n EXAMPLES::\n\n sage: g = graphs.DoubleStarSnark()\n sage: g.order()\n 30\n sage: g.size()\n 45\n ... |
def MeredithGraph():
'\n Return the Meredith Graph.\n\n The Meredith Graph is a 4-regular 4-connected non-hamiltonian graph. For\n more information on the Meredith Graph, see the :wikipedia:`Meredith_graph`.\n\n EXAMPLES::\n\n sage: g = graphs.MeredithGraph()\n sage: g.is_regular(4)\n ... |
def KittellGraph():
'\n Return the Kittell Graph.\n\n For more information, see the `Wolfram page about the Kittel Graph\n <http://mathworld.wolfram.com/KittellGraph.html>`_.\n\n EXAMPLES::\n\n sage: g = graphs.KittellGraph()\n sage: g.order()\n 23\n sage: g.size()\n ... |
def CameronGraph():
'\n Return the Cameron graph.\n\n The Cameron graph is strongly regular with parameters `v = 231, k = 30,\n \\lambda = 9, \\mu = 3`.\n\n For more information on the Cameron graph, see\n `<https://www.win.tue.nl/~aeb/graphs/Cameron.html>`_.\n\n EXAMPLES::\n\n sage: # ne... |
def ChvatalGraph():
"\n Return the Chvatal graph.\n\n Chvatal graph is one of the few known graphs to satisfy Grunbaum's\n conjecture that for every `m`, `n`, there is an `m`-regular, `m`-chromatic\n graph of girth at least `n`. For more information, see the\n :wikipedia:`Chv%C3%A1tal_graph`.\n\n ... |
def ClebschGraph():
'\n Return the Clebsch graph.\n\n See the :wikipedia:`Clebsch_graph` for more information.\n\n EXAMPLES::\n\n sage: g = graphs.ClebschGraph()\n sage: g.automorphism_group().cardinality() # needs sage.groups\n 1920\n sage... |
def CoxeterGraph():
'\n Return the Coxeter graph.\n\n See the :wikipedia:`Coxeter_graph`.\n\n EXAMPLES::\n\n sage: g = graphs.CoxeterGraph()\n sage: g.automorphism_group().cardinality() # needs sage.groups\n 336\n sage: g.girth()\n 7... |
def DejterGraph():
'\n Return the Dejter graph.\n\n The Dejter graph is obtained from the binary 7-cube by deleting a copy of\n the Hamming code of length 7. It is 6-regular, with 112 vertices and 336\n edges. For more information, see the :wikipedia:`Dejter_graph`.\n\n EXAMPLES::\n\n sage: ... |
def DesarguesGraph():
'\n Return the Desargues graph.\n\n PLOTTING: The layout chosen is the same as on the cover of [Har1994]_.\n\n EXAMPLES::\n\n sage: D = graphs.DesarguesGraph()\n sage: L = graphs.LCFGraph(20,[5,-5,9,-9],5) # needs networkx\n s... |
def DurerGraph():
'\n Return the Dürer graph.\n\n For more information, see the :wikipedia:`D%C3%BCrer_graph`.\n\n EXAMPLES:\n\n The Dürer graph is named after Albrecht Dürer. It is a planar graph\n with 12 vertices and 18 edges::\n\n sage: G = graphs.DurerGraph(); G\n Durer graph: Gr... |
def DyckGraph():
'\n Return the Dyck graph.\n\n For more information, see the `MathWorld article on the Dyck graph\n <http://mathworld.wolfram.com/DyckGraph.html>`_ or the\n :wikipedia:`Dyck_graph`.\n\n EXAMPLES:\n\n The Dyck graph was defined by Walther von Dyck in 1881. It has `32` vertices\n ... |
def HortonGraph():
'\n Return the Horton Graph.\n\n The Horton graph is a cubic 3-connected non-hamiltonian graph. For more\n information, see the :wikipedia:`Horton_graph`.\n\n EXAMPLES::\n\n sage: # needs networkx\n sage: g = graphs.HortonGraph()\n sage: g.order()\n 96\n ... |
def EllinghamHorton54Graph():
'\n Return the Ellingham-Horton 54-graph.\n\n For more information, see the :wikipedia:`Ellingham-Horton_graph`.\n\n EXAMPLES:\n\n This graph is 3-regular::\n\n sage: g = graphs.EllinghamHorton54Graph()\n sage: g.is_regular(k=3)\n True\n\n It is 3-... |
def EllinghamHorton78Graph():
'\n Return the Ellingham-Horton 78-graph.\n\n For more information, see the :wikipedia:`Ellingham%E2%80%93Horton_graph`\n\n EXAMPLES:\n\n This graph is 3-regular::\n\n sage: g = graphs.EllinghamHorton78Graph()\n sage: g.is_regular(k=3)\n True\n\n I... |
def ErreraGraph():
'\n Return the Errera graph.\n\n For more information, see the :wikipedia:`Errera_graph`.\n\n EXAMPLES:\n\n The Errera graph is named after Alfred Errera. It is a planar graph on 17\n vertices and having 45 edges::\n\n sage: G = graphs.ErreraGraph(); G\n Errera grap... |
def F26AGraph():
'\n Return the F26A graph.\n\n The F26A graph is a symmetric bipartite cubic graph with 26 vertices and 39\n edges. For more information, see the :wikipedia:`F26A_graph`.\n\n EXAMPLES::\n\n sage: # needs networkx\n sage: g = graphs.F26AGraph(); g\n F26A Graph: Gra... |
def FlowerSnark():
"\n Return a Flower Snark.\n\n A flower snark has 20 vertices. It is part of the class of biconnected cubic\n graphs with edge chromatic number = 4, known as snarks. (i.e.: the Petersen\n graph). All snarks are not Hamiltonian, non-planar and have Petersen graph\n graph minors. S... |
def FolkmanGraph():
'\n Return the Folkman graph.\n\n See the :wikipedia:`Folkman_graph`.\n\n EXAMPLES::\n\n sage: # needs networkx\n sage: g = graphs.FolkmanGraph()\n sage: g.order()\n 20\n sage: g.size()\n 40\n sage: g.diameter()\n 4\n sage... |
def FosterGraph():
'\n Return the Foster graph.\n\n See the :wikipedia:`Foster_graph`.\n\n EXAMPLES::\n\n sage: # needs networkx\n sage: g = graphs.FosterGraph()\n sage: g.order()\n 90\n sage: g.size()\n 135\n sage: g.diameter()\n 8\n sage: g... |
def FranklinGraph():
'\n Return the Franklin graph.\n\n For more information, see the :wikipedia:`Franklin_graph`.\n\n EXAMPLES:\n\n The Franklin graph is named after Philip Franklin. It is a 3-regular graph\n on 12 vertices and having 18 edges::\n\n sage: G = graphs.FranklinGraph(); G\n ... |
def FruchtGraph():
"\n Return a Frucht Graph.\n\n A Frucht graph has 12 nodes and 18 edges. It is the smallest cubic identity\n graph. It is planar and Hamiltonian. See the :wikipedia:`Frucht_graph`.\n\n PLOTTING: Upon construction, the position dictionary is filled to override\n the spring-layout ... |
def GoldnerHararyGraph():
'\n Return the Goldner-Harary graph.\n\n For more information, see the :wikipedia:`Goldner%E2%80%93Harary_graph`.\n\n EXAMPLES:\n\n The Goldner-Harary graph is named after A. Goldner and Frank Harary. It is\n a planar graph having 11 vertices and 27 edges::\n\n sage... |
def GolombGraph():
'\n Return the Golomb graph.\n\n See the :wikipedia:`Golomb_graph` for more information.\n\n EXAMPLES:\n\n The Golomb graph is a planar and Hamiltonian graph with 10 vertices\n and 18 edges. It has chromatic number 4, diameter 3, radius 2 and\n girth 3. It can be drawn in the ... |
def GrayGraph(embedding=1):
'\n Return the Gray graph.\n\n See the :wikipedia:`Gray_graph`.\n\n INPUT:\n\n - ``embedding`` -- integer (default: ``1``); two embeddings are available,\n and can be selected by setting ``embedding`` to 1 or 2\n\n EXAMPLES::\n\n sage: # needs networkx\n ... |
def GrotzschGraph():
'\n Return the Grötzsch graph.\n\n The Grötzsch graph is an example of a triangle-free graph with chromatic\n number equal to 4. For more information, see the\n :wikipedia:`Gr%C3%B6tzsch_graph`.\n\n EXAMPLES:\n\n The Grötzsch graph is named after Herbert Grötzsch. It is a Ha... |
def HeawoodGraph():
"\n Return a Heawood graph.\n\n The Heawood graph is a cage graph that has 14 nodes. It is a cubic symmetric\n graph. (See also the Möbius-Kantor graph, :meth:`~MobiusKantorGraph`). It is\n nonplanar and Hamiltonian. It has diameter 3, radius 3, girth 6, and\n chromatic number 2... |
def HerschelGraph():
'\n Return the Herschel graph.\n\n For more information, see the :wikipedia:`Herschel_graph`.\n\n EXAMPLES:\n\n The Herschel graph is named after Alexander Stewart Herschel. It is a\n planar, bipartite graph with 11 vertices and 18 edges::\n\n sage: G = graphs.HerschelGr... |
def GritsenkoGraph():
"\n Return SRG(65, 32, 15, 16) constructed by Gritsenko.\n\n We took the adjacency matrix from O.Gritsenko's [Gri2021]_ and extracted orbits\n of the automorphism group on the edges.\n\n EXAMPLES::\n\n sage: H = graphs.GritsenkoGraph(); H ... |
def HigmanSimsGraph(relabel=True):
'\n Return the Higman-Sims graph.\n\n The Higman-Sims graph is a remarkable strongly regular graph of degree 22 on\n 100 vertices. For example, it can be split into two sets of 50 vertices\n each, so that each half induces a subgraph isomorphic to the\n Hoffman-S... |
def HoffmanSingletonGraph():
'\n Return the Hoffman-Singleton graph.\n\n The Hoffman-Singleton graph is the Moore graph of degree 7, diameter 2 and\n girth 5. The Hoffman-Singleton theorem states that any Moore graph with\n girth 5 must have degree 2, 3, 7 or 57. The first three respectively are the\n... |
def HoffmanGraph():
'\n Return the Hoffman Graph.\n\n See the :wikipedia:`Hoffman_graph`.\n\n EXAMPLES::\n\n sage: g = graphs.HoffmanGraph()\n sage: g.is_bipartite()\n True\n sage: g.is_hamiltonian() # long time # needs sage.numerical... |
def HoltGraph():
'\n Return the Holt graph (also called the Doyle graph).\n\n See the :wikipedia:`Holt_graph`.\n\n EXAMPLES::\n\n sage: g = graphs.HoltGraph();g\n Holt graph: Graph on 27 vertices\n sage: g.is_regular()\n True\n sage: g.is_vertex_transitive() ... |
def KrackhardtKiteGraph():
'\n Return a Krackhardt kite graph with 10 nodes.\n\n The Krackhardt kite graph was originally developed by David Krackhardt for\n the purpose of studying social networks (see [Kre2002]_ and\n the :wikipedia:`Krackhardt_kite_graph`). It is used to show the distinction\n b... |
def Klein3RegularGraph():
'\n Return the Klein 3-regular graph.\n\n The cubic Klein graph has 56 vertices and can be embedded on a\n surface of genus 3. It is the dual of\n :meth:`~sage.graphs.graph_generators.GraphGenerators.Klein7RegularGraph`.\n For more information, see the :wikipedia:`Klein_gr... |
def Klein7RegularGraph():
'\n Return the Klein 7-regular graph.\n\n The 7-valent Klein graph has 24 vertices and can be embedded on a surface of\n genus 3. It is the dual of\n :meth:`~sage.graphs.graph_generators.GraphGenerators.Klein3RegularGraph`.\n For more information, see the :wikipedia:`Klein... |
def LocalMcLaughlinGraph():
'\n Return the local McLaughlin graph.\n\n The local McLaughlin graph is a strongly regular graph with parameters\n `(162,56,10,24)`. It can be obtained from\n :meth:`~sage.graphs.graph_generators.GraphGenerators.McLaughlinGraph` by\n considering the stabilizer of a poin... |
def LjubljanaGraph(embedding=1):
'\n Return the Ljubljana Graph.\n\n The Ljubljana graph is a bipartite 3-regular graph on 112 vertices and 168\n edges. It is not vertex-transitive as it has two orbits which are also\n independent sets of size 56. See the :wikipedia:`Ljubljana_graph`.\n\n The defau... |
def LivingstoneGraph():
'\n Return the Livingstone Graph.\n\n The Livingstone graph is a distance-transitive graph on 266 vertices whose\n automorphism group is the :class:`J1 group\n <sage.groups.perm_gps.permgroup_named.JankoGroup>`. For more information,\n see the :wikipedia:`Livingstone_graph`.... |
def M22Graph():
'\n Return the M22 graph.\n\n The `M_{22}` graph is the unique strongly regular graph with parameters\n `v = 77, k = 16, \\lambda = 0, \\mu = 4`.\n\n For more information on the `M_{22}` graph, see\n `<https://www.win.tue.nl/~aeb/graphs/M22.html>`_.\n\n EXAMPLES::\n\n sage... |
def MarkstroemGraph():
'\n Return the Markström Graph.\n\n The Markström Graph is a cubic planar graph with no cycles of length 4 nor\n 8, but containing cycles of length 16. For more information, see the\n `Wolfram page about the Markström Graph\n <http://mathworld.wolfram.com/MarkstroemGraph.html... |
def McGeeGraph(embedding=2):
'\n Return the McGee Graph.\n\n See the :wikipedia:`McGee_graph`.\n\n INPUT:\n\n - ``embedding`` -- integer (default: ``2``); two embeddings are available,\n and can be selected by setting ``embedding`` to 1 or 2\n\n EXAMPLES::\n\n sage: # needs networkx\n ... |
def McLaughlinGraph():
"\n Return the McLaughlin Graph.\n\n The McLaughlin Graph is the unique strongly regular graph of parameters\n `(275, 112, 30, 56)`.\n\n For more information on the McLaughlin Graph, see its web page on `Andries\n Brouwer's website <https://www.win.tue.nl/~aeb/graphs/McL.html... |
def MoebiusKantorGraph():
"\n Return a Möbius-Kantor Graph.\n\n A Möbius-Kantor graph is a cubic symmetric graph. (See also the Heawood\n graph). It has 16 nodes and 24 edges. It is nonplanar and Hamiltonian. It\n has diameter 4, girth 6, and chromatic number 2. It is identical to the\n Generalized... |
def MoserSpindle():
'\n Return the Moser spindle.\n\n For more information, see the :wikipedia:`Moser_spindle`.\n\n EXAMPLES:\n\n The Moser spindle is a planar graph having 7 vertices and 11 edges::\n\n sage: # needs sage.symbolic\n sage: G = graphs.MoserSpindle(); G\n Moser spind... |
def NauruGraph(embedding=2):
'\n Return the Nauru Graph.\n\n See the :wikipedia:`Nauru_graph`.\n\n INPUT:\n\n - ``embedding`` -- integer (default: ``2``); two embeddings are available,\n and can be selected by setting ``embedding`` to 1 or 2\n\n EXAMPLES::\n\n sage: g = graphs.NauruGrap... |
def PappusGraph():
'\n Return the Pappus graph, a graph on 18 vertices.\n\n The Pappus graph is cubic, symmetric, and distance-regular.\n\n EXAMPLES::\n\n sage: G = graphs.PappusGraph()\n sage: G.show() # long time # needs sage.plot\n ... |
def PoussinGraph():
'\n Return the Poussin Graph.\n\n For more information on the Poussin Graph, see its corresponding `Wolfram\n page <http://mathworld.wolfram.com/PoussinGraph.html>`_.\n\n EXAMPLES::\n\n sage: g = graphs.PoussinGraph()\n sage: g.order()\n 15\n sage: g.is_... |
def PetersenGraph():
'\n Return the Petersen Graph.\n\n The Petersen Graph is a named graph that consists of 10 vertices and 15\n edges, usually drawn as a five-point star embedded in a pentagon.\n\n The Petersen Graph is a common counterexample. For example, it is not\n Hamiltonian.\n\n PLOTTIN... |
def PerkelGraph():
'\n Return the Perkel Graph.\n\n The Perkel Graph is a 6-regular graph with `57` vertices and `171` edges. It\n is the unique distance-regular graph with intersection array\n `(6,5,2;1,1,3)`. For more information, see the :wikipedia:`Perkel_graph` or\n https://www.win.tue.nl/~aeb... |
def RobertsonGraph():
'\n Return the Robertson graph.\n\n See the :wikipedia:`Robertson_graph`.\n\n EXAMPLES::\n\n sage: # needs networkx\n sage: g = graphs.RobertsonGraph()\n sage: g.order()\n 19\n sage: g.size()\n 38\n sage: g.diameter()\n 3\n ... |
def SchlaefliGraph():
'\n Return the Schläfli graph.\n\n The Schläfli graph is the only strongly regular graphs of parameters\n `(27,16,10,8)` (see [GR2001]_).\n\n For more information, see the :wikipedia:`Schläfli_graph`.\n\n .. SEEALSO::\n\n :meth:`Graph.is_strongly_regular` -- tests wheth... |
def ShrikhandeGraph():
'\n Return the Shrikhande graph.\n\n For more information, see the `MathWorld article on the Shrikhande graph\n <http://mathworld.wolfram.com/ShrikhandeGraph.html>`_ or the\n :wikipedia:`Shrikhande_graph`.\n\n .. SEEALSO::\n\n :meth:`Graph.is_strongly_regular` -- tests... |
def SylvesterGraph():
'\n Return the Sylvester Graph.\n\n This graph is obtained from the Hoffman Singleton graph by considering the\n graph induced by the vertices at distance two from the vertices of an (any)\n edge.\n\n For more information on the Sylvester graph, see\n `<https://www.win.tue.... |
def SimsGewirtzGraph():
'\n Return the Sims-Gewirtz Graph.\n\n This graph is obtained from the Higman Sims graph by considering the graph\n induced by the vertices at distance two from the vertices of an (any)\n edge. It is the only strongly regular graph with parameters `v = 56`,\n `k = 10`, `\\la... |
def SousselierGraph():
'\n Return the Sousselier Graph.\n\n The Sousselier graph is a hypohamiltonian graph on 16 vertices and 27\n edges. For more information, see :wikipedia:`Sousselier_graph` or\n the corresponding French\n `Wikipedia page <https://fr.wikipedia.org/wiki/Graphe_de_Sousselier>`_.\... |
def SzekeresSnarkGraph():
'\n Return the Szekeres Snark Graph.\n\n The Szekeres graph is a snark with 50 vertices and 75 edges. For more\n information on this graph, see the :wikipedia:`Szekeres_snark`.\n\n EXAMPLES::\n\n sage: g = graphs.SzekeresSnarkGraph()\n sage: g.order()\n 5... |
def ThomsenGraph():
"\n Return the Thomsen Graph.\n\n The Thomsen Graph is actually a complete bipartite graph with `(n1, n2) =\n (3, 3)`. It is also called the Utility graph.\n\n PLOTTING: See CompleteBipartiteGraph.\n\n EXAMPLES::\n\n sage: T = graphs.ThomsenGraph()\n sage: T\n ... |
def TietzeGraph():
'\n Return the Tietze Graph.\n\n For more information on the Tietze Graph, see the\n :wikipedia:`Tietze%27s_graph`.\n\n EXAMPLES::\n\n sage: g = graphs.TietzeGraph()\n sage: g.order()\n 12\n sage: g.size()\n 18\n sage: g.diameter()\n ... |
def TruncatedIcosidodecahedralGraph():
'\n Return the truncated icosidodecahedron.\n\n The truncated icosidodecahedron is an Archimedean solid with 30 square\n faces, 20 regular hexagonal faces, 12 regular decagonal faces, 120 vertices\n and 180 edges. For more information, see the\n :wikipedia:`Tr... |
def TruncatedTetrahedralGraph():
'\n Return the truncated tetrahedron.\n\n The truncated tetrahedron is an Archimedean solid with 12 vertices and 18\n edges. For more information, see the :wikipedia:`Truncated_tetrahedron`.\n\n EXAMPLES::\n\n sage: g = graphs.TruncatedTetrahedralGraph(); g\n ... |
def Tutte12Cage():
'\n Return the Tutte 12-Cage.\n\n See the :wikipedia:`Tutte_12-cage`.\n\n EXAMPLES::\n\n sage: # needs networkx\n sage: g = graphs.Tutte12Cage()\n sage: g.order()\n 126\n sage: g.size()\n 189\n sage: g.girth()\n 12\n sage: ... |
def TutteCoxeterGraph(embedding=2):
'\n Return the Tutte-Coxeter graph.\n\n See the :wikipedia:`Tutte-Coxeter_graph`.\n\n INPUT:\n\n - ``embedding`` -- integer (default: ``2``); two embeddings are available,\n and can be selected by setting ``embedding`` to 1 or 2\n\n EXAMPLES::\n\n sag... |
def TutteGraph():
'\n Return the Tutte Graph.\n\n The Tutte graph is a 3-regular, 3-connected, and planar non-hamiltonian\n graph. For more information on the Tutte Graph, see the\n :wikipedia:`Tutte_graph`.\n\n EXAMPLES::\n\n sage: g = graphs.TutteGraph()\n sage: g.order()\n 4... |
def WagnerGraph():
'\n Return the Wagner Graph.\n\n See the :wikipedia:`Wagner_graph`.\n\n EXAMPLES::\n\n sage: # needs networkx\n sage: g = graphs.WagnerGraph()\n sage: g.order()\n 8\n sage: g.size()\n 12\n sage: g.girth()\n 4\n sage: g.diam... |
def WatkinsSnarkGraph():
'\n Return the Watkins Snark Graph.\n\n The Watkins Graph is a snark with 50 vertices and 75 edges. For more\n information, see the :wikipedia:`Watkins_snark`.\n\n EXAMPLES::\n\n sage: g = graphs.WatkinsSnarkGraph()\n sage: g.order()\n 50\n sage: g.... |
def WienerArayaGraph():
'\n Return the Wiener-Araya Graph.\n\n The Wiener-Araya Graph is a planar hypohamiltonian graph on 42 vertices and\n 67 edges. For more information, see the `Wolfram Page on the Wiener-Araya\n Graph <http://mathworld.wolfram.com/Wiener-ArayaGraph.html>`_ or\n :wikipedia:`Wie... |
def _EllipticLinesProjectivePlaneScheme(k):
'\n Pseudo-cyclic association scheme for action of `O(3,2^k)` on elliptic lines.\n\n The group `O(3,2^k)` acts naturally on the `q(q-1)/2` lines of `PG(2,2^k)`\n skew to the conic preserved by it, see Sect. 12.7.B of [BCN1989]_ and\n Sect. 6.D in [BL1984]_. ... |
def MathonStronglyRegularGraph(t):
"\n Return one of Mathon's graphs on 784 vertices.\n\n INPUT:\n\n - ``t`` -- integer; the number of the graph, from 0 to 2\n\n EXAMPLES::\n\n sage: # long time, needs sage.libs.gap\n sage: from sage.graphs.generators.smallgraphs import MathonStronglyReg... |
def JankoKharaghaniGraph(v):
'\n Return a `(936, 375, 150, 150)`-srg or a `(1800, 1029, 588, 588)`-srg.\n\n This functions returns a strongly regular graph for the two sets of\n parameters shown to be realizable in [JK2002]_. The paper also uses a\n construction from [GM1987]_.\n\n INPUT:\n\n - ... |
def JankoKharaghaniTonchevGraph():
'\n Return a `(324,153,72,72)`-strongly regular graph from [JKT2001]_.\n\n Build the graph using the description given in [JKT2001]_, taking sets B1\n and B163 in the text as adjacencies of vertices 1 and 163, respectively, and\n taking the edge orbits of the group `... |
def IoninKharaghani765Graph():
'\n Return a `(765, 192, 48, 48)`-strongly regular graph.\n\n Existence of a strongly regular graph with these parameters was claimed in\n [IK2003]_. Implementing the construction in the latter did not work,\n however. This function implements the following instructions... |
def U42Graph216():
'\n Return a (216,40,4,8)-strongly regular graph from [CRS2016]_.\n\n Build the graph, interpreting the `U_4(2)`-action considered in [CRS2016]_\n as the one on the hyperbolic lines of the corresponding unitary polar space,\n and then doing the unique merging of the orbitals leading... |
def U42Graph540():
'\n Return a (540,187,58,68)-strongly regular graph from [CRS2016]_.\n\n Build the graph, interpreting the `U_4(2)`-action considered in [CRS2016]_\n as the action of `U_4(2)=Sp_4(3)<U_4(3)` on the nonsingular, w.r.t. to the\n Hermitean form stabilised by `U_4(3)`, points of the 3-... |
def AfricaMap(continental=False, year=2018):
'\n Return African states as a graph of common border.\n\n "African state" here is defined as an independent state having the capital\n city in Africa. The graph has an edge between those countries that have\n common *land* border.\n\n INPUT:\n\n - ``... |
def EuropeMap(continental=False, year=2018):
'\n Return European states as a graph of common border.\n\n "European state" here is defined as an independent state having the capital\n city in Europe. The graph has an edge between those countries that have\n common *land* border.\n\n INPUT:\n\n - ... |
def USAMap(continental=False):
"\n Return states of USA as a graph of common border.\n\n The graph has an edge between those states that have common *land* border\n line or point. Hence for example Colorado and Arizona are marked as\n neighbors, but Michigan and Minnesota are not.\n\n INPUT:\n\n ... |
def WorldMap():
'\n Return the Graph of all the countries, in which two countries are adjacent\n in the graph if they have a common boundary.\n\n This graph has been built from the data available\n in The CIA World Factbook [CIA]_ (2009-08-21).\n\n The returned graph ``G`` has a member ``G.gps_coor... |
class GenericGraph(GenericGraph_pyx):
'\n Base class for graphs and digraphs.\n\n .. automethod:: __eq__\n '
graphics_array_defaults = {'layout': 'circular', 'vertex_size': 50, 'vertex_labels': False, 'graph_border': True}
def __init__(self):
'\n Every graph carries a dictionary o... |
def tachyon_vertex_plot(g, bgcolor=(1, 1, 1), vertex_colors=None, vertex_size=0.06, pos3d=None, **kwds):
"\n Helper function for plotting graphs in 3d with\n :class:`~sage.plot.plot3d.tachyon.Tachyon`.\n\n Returns a plot containing only the vertices, as well as the 3d position\n dictionary used for th... |
def graph_isom_equivalent_non_edge_labeled_graph(g, partition=None, standard_label=None, return_relabeling=False, return_edge_labels=False, inplace=False, ignore_edge_labels=False):
"\n Helper function for canonical labeling of edge labeled (di)graphs.\n\n Translates to a bipartite incidence-structure type ... |
class Graph(GenericGraph):
'\n Undirected graph.\n\n A graph is a set of vertices connected by edges. See the\n :wikipedia:`Graph_(mathematics)` for more information. For a collection of\n pre-defined graphs, see the :mod:`~sage.graphs.graph_generators` module.\n\n A :class:`Graph` object has many ... |
def degseq_to_data(degree_sequence):
'\n Convert a degree sequence list to a sorted (max-min) integer data type.\n\n The input degree sequence list (of Integers) is converted to a sorted\n (max-min) integer data type, as used for faster access in the underlying\n database.\n\n INPUT:\n\n - ``deg... |
def data_to_degseq(data, graph6=None):
"\n Convert a database integer data type to a degree sequence list.\n\n INPUT:\n\n - ``data`` -- integer data type (one digit per vertex representing its\n degree, sorted high to low) to be converted to a degree sequence list\n\n - ``graph6`` -- string (defa... |
def graph6_to_plot(graph6):
"\n Return a ``Graphics`` object from a ``graph6`` string.\n\n This method constructs a graph from a ``graph6`` string and returns a\n :class:`sage.plot.graphics.Graphics` object with arguments preset for the\n :meth:`sage.plot.graphics.Graphics.show` method.\n\n INPUT:\... |
def subgraphs_to_query(subgraphs, db):
"\n Return a GraphQuery object required for the induced_subgraphs parameter.\n\n This method constructs and returns a :class:`~GraphQuery` object respecting\n the special input required for the ``induced_subgraphs`` parameter.\n\n INPUT:\n\n - ``subgraphs`` --... |
def graph_db_info(tablename=None):
"\n Return a dictionary of allowed table and column names.\n\n INPUT:\n\n - ``tablename`` -- restricts the output to a single table\n\n EXAMPLES::\n\n sage: sorted(graph_db_info())\n ['aut_grp', 'degrees', 'graph_data', 'misc', 'spectrum']\n\n ::\n\n... |
class GenericGraphQuery(SQLQuery):
def __init__(self, query_string, database=None, param_tuple=None):
"\n A query for a :class:`~GraphDatabase`.\n\n INPUT:\n\n - ``query_string`` -- a string representing the SQL query\n\n - ``database`` -- (default: ``None``); the :class:`~Gra... |
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