Fault-tolerant cycle-embedding of crossed cubes

Abstract

The crossed cube CQ(n) introduced by Efe has many properties similar to those of the popular hypercube. However, the diameter of CQ(n) is about one half of that of the hypercube. Failures of links and nodes in an interconnection network are inevitable. Hence, in this paper, we consider the hybrid fault-tolerant capability of the crossed cube. Letting f(e) and f(v) be the numbers of faulty edges and vertices in CQ(n), we show that a cycle of length 1, for any 4 less than or equal to l less than or equal to V(CQ(n)) - f(v) can be embedded into a wounded crossed cube as long as the total number of faults (f(v) +f(e)) is no more than n - 2, and we say that CQ(n) is (n - 2)-fault-tolerant pancyclic. This result is optimal in the sense that if there are n - 1 faults, there is no guarantee of having a cycle of a certain length in it. (C) 2003 Published by Elsevier B.V.