Fault-tolerant hamiltonian connectivity of the WK-recursive networks

Abstract

Many research on the WK-recursive network has been published during the past several years due to its favorite properties. In this paper, we consider the fault-tolerant hamiltonian connectivity of the WK-recursive network. We use K(d, t) to denote the WK-recursive network of level t, each of which basic modules is a d-vertex complete graph, where d > 1 and t >= 1. The fault-tolerant hamiltonian connectivity H-f(k)(G) is defined to be the maximum integer k such that G is k fault-tolerant hamiltonian connected if G is hamiltonian connected and is undefined otherwise. In this paper, we prove that H-f(k)(K(d, t)) = d - 4 if d >= 4. (C) 2014 Elsevier Inc. All rights reserved.