Sufficient conditions for λ′-optimality in graphs of diameter 2 Original Research Article

For a connected graph G the restricted edge-connectivity λ′(G) is defined as the minimum cardinality of an edge-cut over all edge-cuts S such that there are no isolated vertices in G−S. We call a graph G λ′-optimal, if λ′(G)=ξ(G), where ξ(G) is the minimum edge-degree in G. In 1999, Wang and Li (J. Shanghai Jiaotong Univ. 33(6) (1999) 646) gave a sufficient condition for λ′-optimality in graphs of diameter 2. In this paper, we weaken this condition, and we present some related results. Different examples will show that the results are best possible and independent of each other and of the result of Wang and Li.