TransposePartition[p] reflects a partition p of k parts along the main diagonal, creating a partition with maximum part k.

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.

TreeToCertificate[t] returns a binary string that is a certificate for the tree t such that trees have the same certificate if and only if they are isomorphic.

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

Turan[n, p] constructs the Turán graph, the extremal graph on n vertices that does not contain CompleteGraph[p].

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