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. ...

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

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.

RotateVertices[v, \[Theta]] rotates each vertex position in list v by \[Theta] radians about the origin (0, 0). RotateVertices[g, \[Theta]] rotates the embedding of the graph ...

SamenessRelation[l] constructs a binary relation from a list l of permutations, which is an equivalence relation if l is a permutation group.

SetPartitionToRGF[sp, set] converts the set partition sp of set into the corresponding restricted growth function.

ShowLabeledGraph[g] displays graph g according to its embedding, with each vertex labeled with its vertex number.ShowLabeledGraph[g, l] uses the i\[Null]^th element of list l ...

StableMarriage[mpref, fpref] finds the male optimal stable marriage defined by lists of permutations describing male and female preferences.