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_n. Given a set F comprised of faulty vertices and/or edges in S_n with |F|≤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|F_v| 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|F_v| 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|F_v|+2 to n!-2|F _v| can be embedded.