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.