Sumathi PBrindha T2020-08-282020-08-282016-012347-4890https://ijournals.in/wp-content/uploads/2017/06/12.4117-Brindha.compressed.pdfhttps://dspace.psgrkcw.com/handle/123456789/1186Let 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 numberenDominating NumberNon Split domination numberArticle