GraphDifference[g, h] constructs the graph resulting from subtracting the edges of graph h from the edges of graph g.

InduceSubgraph[g, s] constructs the subgraph of graph g induced by the list of vertices s.

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

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

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

NextGrayCodeSubset[l, s] constructs the successor of s in the Gray code of set l.

NextLexicographicSubset[l, s] gives the lexicographic successor of subset s of set l.

NumberOfCompositions[n, k] counts the number of distinct compositions of integer n into k parts.

NumberOfPartitions[n] counts the number of integer partitions of n.

NumberOfPermutationsByCycles[n, m] gives the number of permutations of length n with exactly m cycles.