A NOTE ON NON-SPLIT SET DOMINATION

Abstract

Let G=(V,E) be a simple, undirected, finite nontrivial graph. A non empty set SV of vertices in a graph G is called a dominating set if every vertex in V-S is adjacent to some vertex in S. The domination number γ(G) of G is the minimum cardinality of a dominating set of G.A dominating set S is called a non split set dominating set if there exists a non empty set R S such that is connected for every set TV-S and the induced subgraph is connected. The minimum cardinality of a nonsplit set dominating set is called the non split set domination number of G and is denoted by γnss (G). In this paper, bounds for γnss (G) and exact values for some particular classes of graphs are found. Keywords: Dominating Number, Non Split domination number