Fault-tolerant edge-bipancyclicity of faulty hypercubes under the conditional-fault model

Abstract

It is well-known that the n-dimensional hypercube Q(n),, is one of the most versatile and efficient interconnection network architecture yet discovered for building massively parallel or distributed systems. Let F be the faulty set of (2,1 and let f(nu), f(e) be the numbers of faulty vertices and faulty edges in F, respectively. An edge e = (x, y) is said to be free if e, x, y are not in F, and a cycle is said to be fault-free if there is no faulty vertex or faulty edge on the cycle. In this paper, we prove that each free edge (x, y) in Qn for n >= 3 lies on a fault-free cycle of any even length from 6 to 2(n) - 2f(nu) if f(nu) + f(e) <= 2n 5, f(e) <= n - 2 and both x and y are incident to at least two free edges. This result confirms a conjecture reported in the literature. (C) 2015 Elsevier Inc. All rights reserved.