On super restricted edge-connectivity of edge-transitive graphs

Let X=(V,E)X=(V,E) be a connected graph. Then XX is called super restricted edge-connected, in short, sup-λ′λ′, if every minimum edge set FF of XX such that X−FX−F is disconnected and every component of X−FX−F has at least two vertices, the set of edges being adjacent to a certain edge with minimum edge degree in XX. In this paper, by studying the λ′λ′-superatoms of XX, we characterize super restricted edge-connected edge-transitive graphs. As a corollary, we present a sufficient and necessary condition for connected vertex-transitive line graphs to be super vertex-connected.