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

AbstractIn 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 f be a faulty vertex in an n-dimensional folded hypercube FQn. We show that FQn−{f} contains a fault-free cycle of every even length from 4 to 2n−2 if n≥3 and, furthermore, every odd length from n+1 to 2n−1 if n≥2 and n is even