McGeeGraph returns the unique (7, 3)-cage, a 3-regular graph with girth 7.

MycielskiGraph[k] returns a triangle-free graph with chromatic number k, for any positive integer k.

RegularQ[g] yields True if g is a regular graph.

RemoveMultipleEdges[g] returns the graph obtained by deleting multiple edges from g.

RemoveSelfLoops[g] returns the graph obtained by deleting self-loops in g.

ReverseEdges[g] flips the directions of all edges in a directed graph.

SmallestCyclicGroupGraph returns a smallest nontrivial graph whose automorphism group is cyclic.

TreeQ[g] yields True if graph g is a tree.

Uniquely3ColorableGraph returns a 12-vertex, triangle-free graph with chromatic number 3 that is uniquely 3-colorable.

UnitransitiveGraph returns a 20-vertex, 3-unitransitive graph, discovered by Coxeter, that is not isomorphic to a 4-cage or a 5-cage.