NthPair[n] returns the n\[Null]^th unordered pair of distinct positive integers, when sequenced to minimize the size of the larger integer. Pairs that have the same larger ...

NumberOfTableaux[p] uses the hook length formula to count the number of Young tableaux with shape defined by partition p.

OddGraph[n] returns the graph whose vertices are the size-(n - 1) subsets of a size-(2 nTraditionalForm\`\[Dash]1) set and whose edges connect pairs of vertices that ...

OrientGraph[g] assigns a direction to each edge of a bridgeless, undirected graph g, so that the graph is strongly connected.

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

SetEdgeLabels[g, l] assigns the labels in l to edges of g.

SetVertexLabels[g, l] assigns the labels in l to vertices of g.

TableauClasses[p] partitions the elements of permutation p into classes according to their initial columns during Young tableaux construction.

TransitiveClosure[g] finds the transitive closure of graph g, the supergraph of g that contains edge {x, y} if and only if there is a path from x to y.

VertexColor is an option that allows the user to associate colors with vertices.