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 (λg(FQn)) of the folded hypercube FQn for g⩽n (denote g by ∑i=0s2ti, where t0=[log2g] and ti=log2g-∑r=0i-12tr). We show that λg(FQn)=g(n+1)-∑i=0sti2ti+∑i=0s2·i·2ti for n⩾6. This result generalizes the previous results by Zhu et al. (2007) for λ3(FQn), and by Hsieh and Tsai (in press) for λ4(FQn), and so on.