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

Josephus[n, m] generates the inverse of the permutation defined by executing every m\[Null]^th member in a circle of n members.

LabeledTreeToCode[g] reduces the tree g to its Prüfer code.

LeviGraph returns the unique (8, 3)-cage, a 3-regular graph whose girth is 8.

LexicographicPermutations[l] constructs all permutations of list l in lexicographic order.

LineGraph[g] constructs the line graph of graph g.

LongestIncreasingSubsequence[p] finds the longest increasing scattered subsequence of permutation p.

MakeSimple[g] gives the undirected graph, free of multiple edges and self-loops derived from graph g.

MaximalMatching[g] gives the list of edges associated with a maximal matching of graph g.

MaximumAntichain[g] gives a largest set of unrelated vertices in partial order g.