Global Vertex-Edge Domination Sets in Total Graph and Product Graph of Path Pn Cycle Cn

Abstract

In a graph G, a subset S of V is Global vertex-edge dominating set if S is vertex-edge dominating set in both G and \({\overline{G}}\).In this paper, we have introduced the new concept, Global vertex-edge dominating set, and identified the Global vertex–edge domination number of Total graph of Kn, K1, n − 1, K n,m, Pn, and Cn. An attempt is made to identify the Global vertex-edge domination number of Cartesian product of path Pn and cycle Cn.