TravelingSalesmanBounds[g] gives upper and lower bounds on a minimum-cost traveling salesman tour of graph g.

Tree is an option that informs certain functions that the user wants the output to be a tree.

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.

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

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

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

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

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

Weak is an option to ConnectedQ that seeks to determine if a directed graph is weakly connected.