Degree Sequence Conditions for Super-Edge-Connected Graphs and Digraphs

Abstract

A graph or a digraph $G$ is called super-edge-connected or super-$\lambda$, if every minimum edge cut consists of edges adjacent to or from a vertex of minimum degree. Clearly, if $G$ is super-$\lambda$, then $\lambda (G)=\delta (G)$, where $\delta (G)$ is the minimum degree and $\lambda (G)$ is the edge-connectivity of $G$.

In this paper, degree sequence conditions for graphs and digraphs as well as for bipartite graphs and digraphs to be super-$\lambda$ are presented.