Fault-tolerant cycles embedded in hypercubes with mixed link and node failures

Let fefe (respectively, fvfv) denote the number of faulty edges (respectively, vertices) of an nn-dimensional hypercube QnQn. In this paper, we prove that every fault-free edge of QnQn for n≥3n≥3 lies on a fault-free cycle of every even length from 4 to 2n−2fv2n−2fv inclusive if fe+fv≤n−2fe+fv≤n−2. Furthermore, we also prove that QnQn for n≥5n≥5 contains a fault-free cycle of every even length from 4 to 2n−2fv2n−2fv inclusive if fe≤n−2fe≤n−2 and fe+fv≤2n−4fe+fv≤2n−4. This result has better tolerance for the faulty components than the degree of the hypercube.