Fault-Free Cycles in Conditional Faulty Folded Hypercubes
نویسندگان
چکیده
An n-dimensional folded hypercube FQn is an attractive variance of an n-dimensional hypercube Qn, which is obtained by a standard hypercube with some extra edges established between its vertices. FQn for any odd n is known to be bipartite. In this paper, for any FQn (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, and when n ≥ 2 is even, there also exists a fault-free cycle of every odd length from n + 1 to 2 − 1. The result is optimal with respect to the number of edges faults tolerated.
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