Hamiltonicity of the WK-Recursive Network with and without Faulty Nodes

• Authors: Jung-Sheng Fu
• Venue: IEEE Transactions on Parallel and Distributed Systems
• Year: 2005

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{\hbox{-}}{\rm{node}} complete graph, where d1 and t \geq 1. In this paper, we first show that K(d, t) is Hamiltonian-connected, where d\geq 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\geq 4. Since the connectivity of K(d, t) is d-1, the result is optimal.