Parent is a tag used as an argument to the function AllPairsShortestPath in order to inform this function that information about parents in the shortest paths is also wanted.

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.

PartialOrderQ[g] yields True if the binary relation defined by edges of the graph g is a partial order, meaning it is transitive, reflexive, and antisymmetric. ...

PartitionLattice[n] returns a Hasse diagram of the partially ordered set on set partitions of 1 through n in which p < q if q is finer than p, that is, each block in q is ...

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

Partitions[n] constructs all partitions of integer n in reverse lexicographic order. Partitions[n, k] constructs all partitions of the integer n with maximum part at most k, ...

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.

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

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

PermutationQ[p] yields True if p is a list representing a permutation and False otherwise.