Fault-tolerant cycle-embedding of crossed cubes

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 l, for any 4?l?|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.