HamiltonianCycle[g] finds a Hamiltonian cycle in graph g if one exists. HamiltonianCycle[g, All] gives all Hamiltonian cycles of graph g.

Vertices[g] gives the coordinates of each vertex of graph g embedded in a plane.Vertices[g, All] gives the embedding of the graph along with graphics options associated with ...

 

LinkRanks[g] gives the link ranks of the directed graph g as a rule list.

ShowGraph[g] displays the graph g. ShowGraph[g, Directed] is obsolete and it is currently identical to ShowGraph[g].

ListGraphs[n, m] returns all nonisomorphic undirected graphs with n vertices and m edges. ListGraphs[n, m, Directed] returns all nonisomorphic directed graphs with n vertices ...

FiniteGraphs produces a convenient list of all the interesting, finite, parameterless graphs built into Combinatorica.

IsomorphismQ[g, h, p] tests if permutation p defines an isomorphism between graphs g and h.

AlternatingPaths[g, start, ME] returns the alternating paths in graph g with respect to the matching ME, starting at the vertices in the list start. The paths are returned in ...

ChromaticPolynomial[g, z] gives the chromatic polynomial P(z) of graph g, which counts the number of ways to color g with, at most, z colors.