On ve-degree and ev-degree of graphs

Let G=(V,E) be a graph with vertex set V and edge set E. The ve-degree of a vertex v∈V equals the number of edges ve-dominated by v and the ev-degree of an edge e∈E equals the number of vertices ev-dominated by e. Recently, Chellali et al. studied the properties of ve-degree and ev-degree of graphs (Chellali et al., 2017). Also they focused on the regularity and irregularity of these types of degrees and proposed several open problems. In this paper, we solve one of them and obtain some results on the regularity and irregularity of ve- and ev-degrees in graphs.