Fault-Free Cycles in Conditional Faulty Folded Hypercubes

Abstract

An n -dimensional folded hypercube FQ n is an attractive variance of an n -dimensional hypercube Q n , which is obtained by a standard hypercube with some extra edges established between its vertices. FQ n for any odd n is known to be bipartite. In this paper, for any FQ n (n *** 2) with at most 2n *** 3 faulty edges in which each vertex is incident with at least two fault-free edges, we prove that there exists a fault-free cycle of every even length from 4 to 2 n , and when n *** 2 is even, there also exists a fault-free cycle of every odd length from n + 1 to 2 n *** 1. The result is optimal with respect to the number of edges faults tolerated.