On embed-ding cycles into faulty twisted cubes

Abstract

The twisted cube TQ(n) is an alternative to the popular hypercube network. Recently, some interesting properties of TQ(n) were investigated. In this paper, we study the pancycle problem on faulty twisted cubes. Let f(e) and f(v) be the numbers of faulty edges and faulty vertices in TQ(n), respectively. We show that, with f(e) + f(v) <= n - 2, a faulty TQ(n) still contains a cycle of length l for every 4 <= l < V(TQ(n)) - f(v) and odd integer n >= 3. (C) 2005 Elsevier Inc. All rights reserved.