 |
SOLUTIONS
|
|
|
|
||
|
|
GraphData |  |
simple graph with n vertices.| "AdjacencyMatrix" | adjacency matrix | |
| "EdgeCount" | total number of edges | |
| "EdgeIndices" | pairs of vertex indices for each edge | |
| "EdgeRules" | edges specified as vertex connectivity rules | |
| "VertexCount" | total number of vertices |
| "AllImages" | list of images of all available layouts for the graph | |
| "AlternateVertexCoordinates" | vertex coordinates for all alternate layouts | |
| "Image" | image of the default layout | |
| "VertexCoordinates" | vertex coordinates for the default layout |
| "ArticulationVertices" | list of vertices whose removal would disconnect the graph | |
| "AutomorphismCount" | order of the vertex automorphism group | |
| "Automorphisms" | vertex permutations corresponding to automorphisms | |
| "Bridges" | list of edges whose removal would disconnect the graph | |
| "ChromaticNumber" | chromatic number | |
| "ChromaticPolynomial" | chromatic polynomial as a pure function | |
| "CliqueNumber" | number of vertices in the largest clique | |
| "CrossingNumber" | minimum crossings in an embedding of the graph | |
| "Degrees" | degrees for each vertex | |
| "Diameter" | the diameter of the graph | |
| "Eccentricities" | eccentricities of each vertex | |
| "EdgeChromaticNumber" | edge chromatic number | |
| "EdgeConnectivity" | minimum edge deletions to disconnect the graph | |
| "Girth" | length of the shortest cycle | |
| "HamiltonianCycleCount" | number of distinct Hamiltonian cycles | |
| "HamiltonianCycles" | lists of Hamiltonian cycles | |
| "HamiltonianPathCount" | number of distinct Hamiltonian paths | |
| "HamiltonianPaths" | lists of Hamiltonian paths | |
| "IndependenceNumber" | size of the largest independent set | |
| "LineGraphName" | name of the line graph corresponding to the graph | |
| "RectilinearCrossingNumber" | minimum crossings in a straight line embedding | |
| "Spectrum" | eigenvalues of the adjacency matrix | |
| "ToroidalCrossingNumber" | minimum crossings in a toroidal embedding | |
| "VertexConnectivity" | minimum vertex deletions to disconnect the graph |
| "AlternateNames" | alternate English names | |
| "AlternateStandardNames" | alternate standard Mathematica names | |
| "Name" | English name | |
| "NotationRules" | rules for notations specifying the graph | |
| "StandardName" | standard Mathematica name |
| "Bipartite" | bipartite (two components connected by every edge) | |
| "Connected" | connected | |
| "Nonplanar" | nonplanar (requires crossings) | |
| "Planar" | planar (no crossings) | |
| "Tree" | tree (no cycles) |
| "Cubic" | each vertex is of degree 3 | |
| "Quartic" | each vertex is of degree 4 | |
| "Quintic" | each vertex is of degree 5 | |
| "Regular" | each vertex is of the same degree |
| "Eulerian" | has a closed cycle containing every edge once | |
| "HamiltonConnected" | every pair of vertices bounds a Hamiltonian path | |
| "Hamiltonian" | has a closed cycle containing every vertex once | |
| "Hypohamiltonian" | one-vertex-removed graphs are Hamiltonian | |
| "Hypotraceable" | one-vertex-removed graphs are traceable | |
| "Noneulerian" | not Eulerian | |
| "Nonhamiltonian" | not Hamiltonian | |
| "SquareFree" | free of 4-cycles | |
| "Traceable" | contains a Hamiltonian path | |
| "TriangleFree" | free of 3-cycles | |
| "Untraceable" | not traceable |
| "DistanceRegular" | all vertices have identical distance sets | |
| "EdgeTransitive" | all edges have identical environments | |
| "Identity" | automorphism group is of order unity | |
| "Semisymmetric" | edge- but not vertex-transitive | |
| "StronglyRegular" | strongly regular | |
| "Symmetric" | both edge- and vertex-transitive | |
| "VertexTransitive" | all vertices have identical environments | |
| "WeaklyRegular" | regular, but not strongly regular |
| "Bicolorable" | two or fewer vertex colors needed | |
| "Bicubic" | bipartite and cubic | |
| "Cage" | smallest graph of a given girth | |
| "CayleyGraph" | Cayley graph | |
| "ClawFree" | free of the claw graph | |
| "Integral" | spectrum consists of integers | |
| "LCF" | describable in LCF notation (cubic Hamiltonian) | |
| "LineGraph" | line graph | |
| "Moore" | graphs with the Moore property | |
| "Perfect" | perfect graph | |
| "SelfComplementary" | isomorphic to its complement | |
| "SelfDual" | isomorphic to its dual | |
| "Snark" | snark graph | |
| "UnitDistance" | embeddable with edges of unit length |
| "Antiprism" | skeleton of an antiprism | |
| "Archimedean" | skeleton of one of the 13 Archimedean solids | |
| "ArchimedeanDual" | skeleton of one of the 13 Archimedean duals | |
| "Platonic" | skeleton of one of the 5 Platonic solids | |
| "Polyhedral" | skeleton of a polyhedron | |
| "Prism" | skeleton of a prism | |
| "RegularPolychoron" | skeleton of one of the 6 regular 4-dimensional solids |
| "Circulant" | n vertices each with identical relative adjacencies | |
| "Complete" | all pairs of vertices are connected | |
| "CompleteBipartite" | all pairs connected across two disjoint sets of vertices | |
| "Crown" | complete bipartite  with horizontal edges removed | |
| "Cycle" | a single cycle through n vertices | |
| "Empty" | n vertices with no edges | |
| "Grid" | an array of points with grid connectivity | |
| "Hypercube" | an n-dimensional hypercube | |
| "Ladder" | a 2 n-vertex ladder graph | |
| "MoebiusLadder" | an n-sided prism graph with a half-twist | |
| "Path" | an n-vertex tree with no branches | |
| "Star" | a center vertex connected to n-1 vertices | |
| "Wheel" | a cycle with all vertices connected to a center |
| "Description" | short textual description of the property | |
| "LongDescription" | longer textual description of the property | |
| "Note" | additional information about the property |
| © 2013 Wolfram Research, Inc. | 
|
EXAMPLES
Basic Examples 
Scope 