JMAT_V2_N3_RP3 D.R. Robert Joan Journal on Mathematics 2277-5137 2 3 38 49 Point Set Domination, Strong Point Set Dominating Set, Connected Graph, Separable Graph, Strong Point Set Domination Number, Blocks, Bounds, Dominating Set Let G be a connected graph. A set D V(G) is a point-set dominating set (psd-set) of G if for every set S V – D, there exists a vertex v D such that the subgraph induced by S {v} is connected. The point-set domination number γ (G) p of G is the minimum cardinality of a psd-set. This paper provides a comprehensive treatment of point set domination in graphs. First introduce the point-set domination number of a graph G, and determine this number for various known graphs. The relationship between set domination number with r point set domination number, point-set domination number and also few results regarding point-set are given as statements. Also In this paper the investigator say about global set-domination number γ and global point-set domination number γ of a graph G and determine these sg pg numbers for various known graphs and obtain some bounds for the graph G of diameters 3 and 4 in terms of γ. Finally the concept of the strong point-set domination number of a graph G is introduced, and its exact value is determined for some known graphs. July - September 2013 Copyright © 2013 i-manager publications. All rights reserved. i-manager Publications http://www.imanagerpublications.com/Article.aspx?ArticleId=2460