Conditional fault-tolerant edge-bipancyclicity of hypercubes with faulty vertices and edges

摘要

Let F be a faulty set in an n-dimensional hypercube Q(n) such that in Q(n) - F each vertex is incident to at least two edges, and let f(v), f(e) be the numbers of faulty vertices and faulty edges in F, respectively. In this paper, we consider the fault-tolerant edge-bipancyclicity of hypercubes. It is shown that each edge in Q(n) - F for n >= 3 lies on a fault-free cycle of any even length from 6 to 2(n) - 2f(v) if f(v) + f(e) <= 2n - 5. This gives an answer for a problem proposed by Yang et al. (2016) [33]. (C) 2016 Elsevier B.V. All rights reserved.