Nonsplit domination number in vertex semi-middle graph

Abstract

Let G(p, q) be a connected graph and Mv (G) be its corresponding vertex semi middle graph. A dominating set D⊆V[Mv (G)] is Nonsplit dominating set 〈V[Mv (G)]-D〉 is connected. The minimum size of D is called the Nonsplit domination number of Mv (G) and is denoted by γns [Mv (G)]. In this paper we obtain several results on Nonsplit domination number.