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.

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.

VertexLabelPosition is an option that allows the user to place a vertex label in a certain position relative to the vertex.

VertexWeight is an option that allows the user to associate weights with vertices.

WeightingFunction is an option to the functions SetEdgeWeights and SetVertexWeights that tells the functions how to compute edge weights and vertex weights, respectively.