On reliability of the folded hypercubes in terms of the extra edge-connectivity

For a graph G and a non-negative integer g, the g-extra edge connectivity of G is the minimum cardinality of a set of edges in G, if it exists, whose deletion disconnects G and each remaining component will have at least g vertices. The extra edge-connectivity is an important parameters for the reliability evaluation of interconnection networks. In this paper, we explore g-extra-edge-connectivity (lambda(g)(FQ(n))) of the folded hypercube FQ(n) for g <= n (denote g by Sigma(s)(i)=(0)2(ti), where t(0) = [log(2)g] and t(i) = [log(2) (g - Sigma(i-1)(r=0) 2(tr))]). We show that lambda(g)(FQ(n)) = g(n +1) - (Sigma(s)(i=0)t(i)2(ti) + Sigma(s)(i=0)2 .i .2(ti)) for n >= 6. This result generalizes the previous results by Zhu et al. (2007) for lambda(3)(FQ(n)), and by Hsieh and Tsai (in press) for lambda(4)(FQ(n)), and so on. (C) 2014 Elsevier Inc. All rights reserved.