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

An outer-connected vertex edge dominating set (OCVEDS) for an arbitrary graph G is a set D ⊂ V ( 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 the cardinality of a minimum OCVEDS of G , denoted by γ o c v e ( G ) . In this paper, we give the outer-connected vertex edge dominating set in lexicographic product of graphs.