Edge fault tolerance of graphs with respect to super edge connectivity

Abstract: A connected graph is super edge connected (super- for short) if every minimum edge cut of is the set of edges incident with some vertex. We define a super- graph to be -super- if is still super- for any edge subset with . The maximum integer of such , written as , is said to be the edge fault tolerance of with respect to the super- property. In this paper, we study the bounds for , showing that . More refined bounds are obtained for regular graphs and Cartesian product graphs. Exact values of are obtained for edge transitive graphs. [Copyright &y& Elsevier]