Laceability in the Total Graph of Some Classes of Graphs

A connected graph G is termed Hamiltonian-t*-laceable if there exists in it a Hamiltonian path between at least one pair of vertices u and v with the property d(u, v) = t, 1 t diamG, where t is a positive integer. If G is Hamiltonian-t*- laceable for all t such that 1 t diamG, we call G t*-connected. In this paper, we show that the total graph of the wheel graph W1 n is t*-connectedfor all n 3 and the total graph of the (W1n, k), k = 1 is t*-connected for n 3. We also show that the total graph of (Gc)2n is t*-connectedfor all n 3.