Abstract
Let G=(V,E) be a graph with vertex set V and edge set E. A vertex v∈Vve-dominates every edge incident to it as well as every edge adjacent to these incident edges. The vertex–edge degree of a vertex v is the number of edges ve-dominated by v. Similarly, an edge e=uv ev-dominates the two vertices u and v incident to it, as well as every vertex adjacent to u or v. The edge–vertex degree of an edge e is the number of vertices ev-dominated by edge e. In this paper we introduce these types of degrees and study their properties.
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