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 ( λ g ( FQ n ) ) of the folded hypercube FQ n for g ≤ n (denote g by ? i = 0 s 2 t i , where t 0 = log 2 g ] and t i = log 2 g - ? r = 0 i - 1 2 t r ). We show that λ g ( FQ n ) = g ( n + 1 ) - ? i = 0 s t i 2 t i + ? i = 0 s 2 ? i ? 2 t i for n ? 6 . This result generalizes the previous results by Zhu et al. (2007) for λ 3 ( FQ n ) , and by Hsieh and Tsai (in press) for λ 4 ( FQ n ) , and so on.

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