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.
1970-2025 CP (Manitoba, Canada) unless otherwise stated.