TransitiveReduction[g] finds a smallest graph that has the same transitive closure as g.

TransposeTableau[t] reflects a Young tableau t along the main diagonal, creating a different tableau.

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

TravelingSalesman[g] finds an optimal traveling salesman tour in graph g.

TreeIsomorphismQ[t_1, t_2] yields True if the trees t_1 and t_2 are isomorphic. It yields False otherwise.

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.