Fault-tolerant hamiltonian connectivity of the WK-recursive networks

A graph G is said to be Hamiltonian-connected if there is a Hamiltonian path between every two distinct nodes of G. Let F denote the set of faulty nodes of G. Then, G is |F |-node Hamiltonianconnected if G−F is Hamiltonian-connected. We use K(d, t) to denote a WK-recursive network of level t, each of whose basic modules is a d-node complete graph. Compared with other networks, it is rather difficult to construct a Hamiltonian path between arbitrary two nodes in a faulty WKrecursive network. In this paper, we show that K(d, t) is (d − 4)-node Hamiltonian-connected. Since the connectivity of K(d, t) is d − 1, the result is optimal in the worst case.