Super restricted edge connectivity of regular edge-transitive graphs

Abstract: An edge cut of a connected graph is called restricted if it separates this graph into components each having order at least 2; a graph is super restricted edge connected if contains an isolated edge for every minimum restricted edge cut of . It is proved in this paper that a connected regular edge-transitive graph of valency at least 3 is not super restricted edge connected if and only if it is either the three dimensional hypercube, or a tetravalent edge-transitive graph of girth 3 and of order at least 6. As a result, there are infinitely many -regular Hamiltonian graphs with which are not super restricted edge connected. This answers negatively a question in [J. Ou, F. Zhang, Super restricted edge connectivity of regular graphs, Graphs & Combin. 21 (2005) 459–467] regarding the relationship between restricted edge connected graphs and Hamiltonian graphs. [Copyright &y& Elsevier]