On veve-degrees and evev-degrees in graphs

Let G=(V,E)G=(V,E) be a graph with vertex set VV and edge set EE. A vertex v∈Vv∈Vveve-dominates every edge incident to it as well as every edge adjacent to these incident edges. The vertex–edge degree of a vertex vv is the number of edges veve-dominated by vv. Similarly, an edge e=uve=uv evev-dominates the two vertices uu and vv incident to it, as well as every vertex adjacent to uu or vv. The edge–vertex degree of an edge ee is the number of vertices evev-dominated by edge ee. In this paper we introduce these types of degrees and study their properties.