Sufficient conditions for super-edge-connected graphs depending on the clique number

Abstract

Let $\delta (G)$ and $\lambda (G)$ be the minimum degree and edge-connectivity of a graph $G$, respectively. A graph $G$ is maximally edge-connected if $\lambda (G)=\delta (G)$ and super-edge-connected if every minimum edge cut consists of edges adjacent to a vertex of minimum degree.

In this paper, sufficient conditions for super-edge-connected graphs depending on the clique number and the minimum degree are presented. These results show that some known sufficient conditions for maximally edge-connected graphs even lead to super-edge-connected graphs.