Bipanconnectivity of faulty hypercubes with minimum degree

In this paper, we consider the conditionally faulty hypercube Q(n) with n >= 2 where each vertex of Q(n) is incident with at least m fault-free edges, 2 <= m <= n - 1. We shall generalize the limitation m >= 2 in all previous results of edge-bipancyclicity. We also propose a new edge-fault-tolerant bipanconnectivity called k-edge-fault-tolerant bipanconnectivity. A bipartite graph is k-edge-fault-tolerant bipanconnected if G - F remains bipanconnected for any F subset of E(G) with vertical bar F vertical bar <= k. For every integer m, under the same hypothesis, we show that Qn is (n - 2)-edge-fault-tolerant edge-bipancyclic and bipanconnected, and the results are optimal with respect to the number of edge faults tolerated. This not only improves some known results on edge-bipancyclicity and bipanconnectivity of hypercubes, but also simplifies the proof. (C) 2011 Elsevier Inc. All rights reserved.