Highly fault-tolerant cycle embeddings of hypercubes

Abstract: The hypercube Q n is one of the most popular networks. In this paper, we first prove that the n-dimensional hypercube is 2n −5 conditional fault-bipancyclic. That is, an injured hypercube with up to 2n −5 faulty links has a cycle of length l for every even 4⩽ l ⩽2 n when each node of the hypercube is incident with at least two healthy links. In addition, if a certain node is incident with less than two healthy links, we show that an injured hypercube contains cycles of all even lengths except hamiltonian cycles with up to 2n −3 faulty links. Furthermore, the above two results are optimal. In conclusion, we find cycles of all possible lengths in injured hypercubes with up to 2n −5 faulty links under all possible fault distributions. [Copyright &y& Elsevier]