TriangleInequalityQ[g] yields True if the weights assigned to the edges of graph g satisfy the triangle inequality.

UnionSet[a, b, s] merges the sets containing a and b in union-find data structure s.

Uniquely3ColorableGraph returns a 12-vertex, triangle-free graph with chromatic number 3 that is uniquely 3-colorable.

UnitransitiveGraph returns a 20-vertex, 3-unitransitive graph, discovered by Coxeter, that is not isomorphic to a 4-cage or a 5-cage.

UnrankGrayCodeSubset[n, l] gives the n\[Null]^th subset of list l, listed in Gray code order.

UnrankKSubset[m, k, l] gives the m\[Null]^th k-subset of set l, listed in lexicographic order.

UnrankSubset[n, l] gives the n\[Null]^th subset of list l, listed in some canonical order.

UnweightedQ[g] yields True if all edge weights are 1 and False otherwise.

VertexCoverQ[g, c] yields True if the vertices in list c define a vertex cover of graph g.

V[g] gives the order or number of vertices of the graph g.