Edge fault tolerance of graphs with respect to super edge connectivity

A connected graph G is super edge connected (super-λ for short) if every minimum edge cut of G is the set of edges incident with some vertex. We define a super-λ graph G to be m-super-λ if G−S is still super-λ for any edge subset S with |S|⩽m. The maximum integer of such m, written as Sλ(G), is said to be the edge fault tolerance of G with respect to the super-λ property. In this paper, we study the bounds for Sλ(G), showing that min{λ′(G)−δ(G)−1,δ(G)−1}⩽Sλ(G)⩽δ(G)−1. More refined bounds are obtained for regular graphs and Cartesian product graphs. Exact values of Sλ are obtained for edge transitive graphs.