Let G be a connected k(≥3)-regular graph with girth g. A set S of the edges in G is called an R_2-edge-cut if G-S is disconnected and contains neither an isolated vertex nor a undergo vertex. The R_2-edge-connectivity of G, denoted by λ"(G), is the minimum cardinality over all R_2-edge-cus, which is an important measure for fault-tolerance of computer interconnection networks. In this paper, λ "(G)=g(2k-2) for any 2k-regular connected graph G(≠K_5) that is either edge-transitive or vertex-transitive and g≥5 is given.
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