Split Domination Number in Edge Semi-Middle Graph

Abstract

Let G = (p, q) be a connected graph and Me(G) be its corresponding edge semi-middle graph. A dominating set D ⊆ V [Me(G)] is split dominating set V [Me(G)] – D is disconnected. The minimum size of D is called the split domination number of Me(G) and is denoted by γs[Me(G)]. In this paper we obtain several results on split domination number.