Every edge lies on cycles embedding in folded hypercubes with vertex-fault-tolerant

The folded hypercube is a well-known variation of hypercube structure and can be constructed from a hypercube by adding a link to every pair of vertices with complementary addresses. An n-dimensional folded hypercube (FQ(n) for short) for any odd n is known to be bipartite. In this paper, let f be a faulty vertex in FQ(n). It has been shown that (1) Every edge of FQ(n) - {f} lies on a fault-free cycle of every even length l with 4 <= l <= 2(n) - 2 where n >= 3; (2) Every edge of FQ(n) - {f} lies on a fault-free cycle of every odd length l with n + 1 <= l <= 2(n) - 1, where n >= 2 is even. In terms of every edge lies on a fault-free cycle of every odd length in FQ(n) - {f}, our result improves the result of Cheng et al. (2013) where odd cycle length up to 2(n) - 3. (C) 2015 Elsevier B.V. All rights reserved.