Edge-bipancyclicity of star graphs with faulty elements

In this paper, we investigate the fault-tolerant edge-bipancyclicity of an n-dimensional star graph S. Given a set F comprised of faulty vertices and/or edges in S, with vertical bar F vertical bar <= n - 3 and any fault-free edge e in S-n - F, we show that there exist cycles of every even length from 6 to n! - 2 vertical bar F-v vertical bar in S-n - F containing e, where n >= 3. Our result is optimal because the star graph is both bipartite and regular with the common degree n - 1. The length of the longest fault-free cycle in the bipartite S-n is n! - 2 vertical bar F-v vertical bar in the worst case, where all faulty vertices are in the same partite set. We also provide some sufficient conditions from which longer cycles with length from n! - 2 vertical bar F-v vertical bar + 2 to n! - 2 vertical bar F-v vertical bar can be embedded. (C) 2011 Elsevier B.V. All rights reserved.