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

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

PermutationToTableaux[p] returns the tableaux pair that can be constructed from p using the Robinson\[Dash]Schensted\[Dash]Knuth correspondence.

PermutationType[p] returns the type of permutation p.

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.

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.