The outer-connected vertex edge domination number in Cartesian product graphs

Abstract

Let G be a simple, finite and connected graph. An outer-connected vertex edge dominating set, abbreviated OCVEDS of G is a subset D of vertices of G such that D is a vertex edge dominating set and the graph G\\D is connected. The outer-connected vertex edge domination number of G is a minimum cardinality of a OCVEDS of G and is denoted by . This paper focuses on the OCVEDS in Cartesian product of graphs.