Super s-restricted edge-connectivity of vertex-transitive graphs

Let G be a connected graph with vertex-set V (G) and edge-set E(G). A subset F of E(G) is an s-restricted edge-cut of G if G - F is disconnected and every component of G - F has at least s vertices. Let λs(G) be the minimum size of all s-restricted edge-cuts of G and ξs(G)=min{|[X, V (G)\X]|: |X| = s, G[X] is connected}, where [X, V (G)\X] is the set of edges with exactly one end in X. A graph G with an s-restricted edge-cut is called super s-restricted edge-connected, in short super-λs, if λs(G) = ξs(G) and every minimum s-restricted edge-cut of G isolates one component G[X] with |X| = s. It is proved in this paper that a connected vertex-transitive graph G with degree k > 5 and girth g > 5 is super-λs for any positive integer s with s ⩽ 2g or s ⩾ 10 if k = g = 6.