EmptyQ[g] yields True if graph g contains no edges.

EulerianCycle[g] finds an Eulerian cycle of g if one exists.

HamiltonianPath[g] finds a Hamiltonian path in graph g if one exists. HamiltonianPath[g, All] gives all Hamiltonian paths of graph g.

IndependentSetQ[g, i] yields True if the vertices in list i define an independent set in graph g.

InvolutionQ[p] yields True if permutation p is its own inverse.

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

MinimumVertexColoring[g] returns a minimum vertex coloring of g. MinimumVertexColoring[g, k] returns a k-coloring of g, if one exists.

MultipleEdgesQ[g] yields True if g has multiple edges between pairs of vertices. It yields False otherwise.

PermutationGroupQ[l] yields True if the list of permutations l forms a permutation group.

PermutationQ[p] yields True if p is a list representing a permutation and False otherwise.