Super-connected edge transitive graphs

A graph G is said to be super-connected if any minimum cut of G isolates a vertex. In a previous work due to the second author of this note, super-connected graphs which are both vertex transitive and edge transitive are characterized. In this note, we generalize the characterization to edge transitive graphs which are not necessarily vertex transitive, showing that the only irreducible edge transitive graphs which are not super-connected are the cycles C-n (n >= 6) and the line graph of the 3-cube, where irreducible means the graph has no vertices with the same neighbor set. Furthermore, we give some sufficient conditions for reducible edge transitive graphs to be super-connected. (C) 2007 Elsevier B.V. All rights reserved.