TreeQ[g] yields True if graph g is a tree.

TutteGraph returns the Tutte graph, the first known example of a 3-connected, 3-regular, planar graph that is non-Hamiltonian.

UndirectedQ[g] yields True if graph g is undirected.

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.

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.

UpperLeft is a value that options VertexNumberPosition, VertexLabelPosition, and EdgeLabelPosition can take on in ShowGraph.