Hamiltonian connectivity of the WK-recursive network with faulty nodes

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 image-node Hamiltonian-connected if image is Hamiltonian-connected. We use image 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 two arbitrary nodes in a faulty WK-recursive network. In this paper, we show that image is image-node Hamiltonian-connected. Since the connectivity of image is image, the result is optimal in the worst case.