NumberOfDerangements[n] counts the derangements on n elements, that is, the permutations without any fixed points.

NumberOfSpanningTrees[g] gives the number of labeled spanning trees of graph g.

PermutationGraph[p] gives the permutation graph for the permutation p.

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

PermutationType[p] returns the type of permutation p.

PlanarQ[g] yields True if graph g is planar, meaning it can be drawn in the plane so no two edges cross.

PseudographQ[g] yields True if graph g is a pseudograph, meaning it contains self-loops.

Radius[g] gives the radius of graph g, the minimum eccentricity of any vertex of g.

RandomComposition[n, k] constructs a random composition of integer n into k parts.

RandomKSubset[l, k] gives a random subset of set l with exactly k elements.