Abstract
Let D be a finite and simple digraph with vertex set V(D). For a vertex v∈V(D), the degree d(v) of v is defined as the minimum value of its out-degree d+(v) and its in-degree d−(v). If D is a graph or a digraph with minimum degree δ and edge-connectivity λ, then λ≤δ. A graph or a digraph is maximally edge-connected if λ=δ. A graph or a digraph is called super-edge-connected if every minimum edge-cut consists of edges adjacent to or from a vertex of minimum degree.In this note we present degree sequence conditions for maximally edge-connected and super-edge-connected digraphs depending on the clique number of the underlying graph.
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