Edge-Vertex Domination in Graphs

Abstract

In this paper we continue the study of ev-domination (edge-vertex domination) in graphs. We give a characterization of minimal ev-dominating sets in graphs. In particular we prove that in a graph with minimum vertex degree greater than or equal to 2, the complement of a minimal ev-dominating set is an edge dominating set. We also state and prove necessary and sufficient condition under which the ev-domination number increases or decreases when a vertex is removed from the graph. We also consider the operation of removing an edge from the graph and prove that the ev-domination number does not decrease when an edge is removed from the graph.