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 oc ve (G). In this paper, we give the outer-connected vertex edge dominating set in lexicographic product of graphs.
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