Hamiltonicity of the WK-recursive network with and without faulty nodes

Recently, the WK-recursive network has received much attention due to its many favorable properties such as a high degree of scalability. By K(d, t), we denote the WK-recursive network of level t, each of whose basic modules is a d-node complete graph, where d > 1 and t >= 1. In this paper, we first show that K(d, t) is Hamiltonian-connected, where d >= 4. A network is Hamiltonian-connected if it contains a Hamiltonian path between every two distinct nodes. In other words, a Hamiltonian-connected network can embed the longest linear array between any two distinct nodes with dilation, congestion, load, and expansion all equal to one. Then, we construct fault-free Hamiltonian cycles in K(d, t) with at most d - 3 faulty nodes, where d >= 4. Since the connectivity of K(d, t) is d - 1, the result is optimal.