2-restricted Edge Connectivity of Vertex-transitive Graphs

The 2-restricted edge-connectivity λ′′ of a graph G is defined to be the minimum cardinality |S| of a set S of edges such thatG−S is disconnected and is of minimum degree at least two. It is known that λ′′ ≤ g(k − 2) for any connected k-regular graph G of girth g other than K4, K5 and K3,3, where k ≥ 3. In this paper, we prove the following result: For a connected vertex-transitive graph of order n ≥ 7, degree k ≥ 6 and girth g ≥ 5, we have λ′′ = g(k−2). Moreover, if k ≥ 6 and λ′′ < g(k−2), then λ′′|n or λ′′|2n.