OutDegree[g, n] returns the out-degree of vertex n in directed graph g. OutDegree[g] returns the sequence of out-degrees of the vertices in directed graph g.

PairGroup[g] returns the group induced on 2-sets by the permutation group g. PairGroup[g, Ordered] returns the group induced on ordered pairs with distinct elements by the ...

ParentsToPaths[l, i, j] takes a list of parents l and returns the path from i to j encoded in the parent list. ParentsToPaths[l, i] returns the paths from i to all vertices.

PartitionQ[p] yields True if p is an integer partition. PartitionQ[n, p] yields True if p is a partition of n.

PerfectQ[g] yields True if g is a perfect graph, meaning that for every induced subgraph of g the size of a largest clique equals the chromatic number.

PermutationWithCycle[n, {i, j, ...}] gives a size-n permutation in which {i, j, ...} is a cycle and all other elements are fixed points.

PermuteSubgraph[g, p] permutes the vertices of a subgraph of g induced by p according to p.

PetersenGraph returns the Petersen graph, a graph whose vertices can be viewed as the size-2 subsets of a size-5 set with edges connecting disjoint subsets.

RandomSubset[l] creates a random subset of set l.

RankBinarySubset[l, s] gives the rank of subset s of set l in the ordering of subsets of l, obtained by interpreting these subsets as binary string representations of ...