Fault-tolerant cycle-embedding of crossed cubes

The crossed cube CQn introduced by Efe has many properties similar to those of the popular hypercube. However, the diameter of CQn 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 fe and fv be the numbers of faulty edges and vertices in CQn, we show that a cycle of length l, for any 4 l |V (CQn)|−fv , can be embedded into a wounded crossed cube as long as the total number of faults (fv + fe) is no more than n− 2, and we say that CQn 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.  2003 Published by Elsevier B.V.