1-vertex-fault-tolerant cycles embedding on folded hypercubes

In this paper, we focus on a hypercube-like structure, the folded hypercube, which is basically a standard hypercube with some extra links between its nodes. Let ff be a faulty vertex in an nn-dimensional folded hypercube FQnFQn. We show that FQn−{f}FQn−{f} contains a fault-free cycle of every even length from 4 to 2n−22n−2 if n≥3n≥3 and, furthermore, every odd length from n+1n+1 to 2n−12n−1 if n≥2n≥2 and nn is even.