Cycles embedding in folded hypercubes under the conditional fault model

A faulty network G is under the conditional fault model, i.e., every fault-free vertex of G is incident to at least two fault-free edges. Let FFv and FFe be the set of faulty vertices and faulty edges in FQ, respectively. In this paper, we consider FQ(n) under the conditional fault model and prove that if vertical bar FFv vertical bar + vertical bar FFe vertical bar <= 2n - 4 and n >= 3, then FQ(n) - FFv - FFe contains a fault-free cycle of every even length from 4 to 2(n) - 2 vertical bar FFv vertical bar; if vertical bar FFv vertical bar + vertical bar FFe vertical bar <= 2n - 5 and n >= 4 is even, then FQ(n) - FFv - FFe contains a fault-free cycle of every odd length from n + 1 to 2(n) 2 vertical bar FFv vertical bar - 1. (C) 2017 Elsevier B.V. All rights reserved.