TreeToCertificate[t] returns a binary string that is a certificate for the tree t such that trees have the same certificate if and only if they are isomorphic.

Turan[n, p] constructs the Turán graph, the extremal graph on n vertices that does not contain CompleteGraph[p].

TwoColoring[g] finds a two-coloring of graph g if g is bipartite. It returns a list of the labels 1 and 2 corresponding to the vertices.

UnrankBinarySubset[n, l] gives the n\[Null]^th subset of list l, listed in increasing order of integers corresponding to the binary representations of the subsets.

UnrankSetPartition[r, s, k] finds a k-block set partition of s with rank r. UnrankSetPartition[r, n, k] finds a k-block set partition of {1, 2, ..., n} with rank r.

UnrankPermutation[r, l] gives the r\[Null]^th permutation in the lexicographic list of permutations of list l. UnrankPermutation[r, n] gives the r\[Null]^th permutation in ...

UnrankSetPartition[r, set] finds a set partition of set with rank r. UnrankSetPartition[r, n] finds a set partition of {1, 2, ..., n} with rank r.

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

VertexConnectivityGraph[g] returns a directed graph that contains an edge corresponding to each vertex in g and in which edge-disjoint paths correspond to vertex-disjoint ...

VertexLabelColor is an option that allows the user to associate different colors to vertex labels.