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

Abstract

Let F be a faulty set in an n-dimensional hypercube Qn such that in Qn−F each vertex is incident to at least two edges, and let fv, fe 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 Qn−F for n≥3 lies on a fault-free cycle of any even length from 6 to 2n−2fv if fv+fe≤2n−5. This gives an answer for a problem proposed by Yang et al. (2016) [33].