Fault-tolerant cycles embedded in hypercubes with mixed link and node failures

Let f(e) (respectively, f(v)) denote the number of faulty edges (respectively, vertices) of an n-dimensional hypercube Q(n) - In this paper, we prove that every fault-free edge of Q(n) for n >= 3 lies on a fault-free cycle of every even length from 4 to 2(n) - 2f(v) inclusive if f(e) + f(v) <= n - 2. Furthermore, we also prove that Qn for n >= 5 contains a fault-free cycle of every even length from 4 to 2(n) - 2f(v) inclusive if f(e) <= n - 2 and f(e) + f(v) <= 2n - 4. This result has better tolerance for the faulty components than the degree of the hypercube. (c) 2007 Elsevier Ltd. All rights reserved.