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.

TwoColoring[g] finds a two-coloring of graph g if g is bipartite. It returns a list of the labels 1 and 2 corresponding to the vertices.

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.