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

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.

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

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.

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

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 ...

UnrankRGF[r, n] returns a restricted growth function defined on the first n natural numbers whose rank is r.

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.

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.