ThomassenGraph returns a hypotraceable graph, a graph G that has no Hamiltonian path but whose subgraph G - v for every vertex v has a Hamiltonian path.

TopologicalSort[g] gives a permutation of the vertices of the directed acyclic graph g such that an edge (i, j) implies that vertex i appears before vertex j.

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

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.

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

UnrankSetPartition[r, s, k] finds a k-block set partition of s with rank r. UnrankSetPartition[r, n, k] finds a k-block set partition of {1, 2, ..., n} with rank r.

UnrankSetPartition[r, set] finds a set partition of set with rank r. UnrankSetPartition[r, n] finds a set partition of {1, 2, ..., n} with rank r.

VertexConnectivity[g] gives the minimum number of vertices whose deletion from graph g disconnects it. VertexConnectivity[g, Cut] gives a set of vertices of minimum size ...

Vertices[g] gives the coordinates of each vertex of graph g embedded in a plane.Vertices[g, All] gives the embedding of the graph along with graphics options associated with ...

Wheel[n] constructs a wheel on n vertices, which is the join of CompleteGraph[1] and Cycle[n - 1].