JMAT_V3_N1_A2 D.R. Robert Joan Y. Sheeja Journal on Mathematics 2277-5137 3 1 7 13 Dominating Set, Total Dominating Set, Global Dominating Set, Split Dominating Set, Strong Split Dominating Set, Nilprivate Neighbour, Nil Private Neighbour Dominating Set A dominating set D V is said to be a nilprivate neighbour dominating set if, for every vertex u in D has no private neighbour in V-D. The nilprivate neighbour domination number (G) is the minimum cardinality of a nilprivate npn neighbour dominating set. A dominating set D V of a graph G is a non-split dominating set if the induced sub-graph is connected. The non-split domination number (G) is the minimum cardinality of a non-split dominating set of G. A ns dominating set D V of a graph G is a strong non-split dominating set if the induced sub-graph is complete. The strong non-split domination number sns(G) is the minimum cardinality of a strong non-split dominating set of G. The dominating set D V of a graph G is a vertex set dominating set if for any set S V-D, there exists a vertex vD such that the induced sub-graph is connected. The vertex set domination number (G) is the minimum cardinality of a vs vertex set dominating set of G. A dominating set D of a graph is a strong non-split dominating set if the induced sub-graph is complete. The strong non-split domination number of G is the minimum cardinality of a strong sns non-split dominating set of G. Here, the authors state some definitions and statements related to the Nilprivate neighbour domination and strong non-split domination number in graphs. In conclusion, the authors state the domination of strong non-split domination graphs. January - March 2014 Copyright © 2014 i-manager publications. All rights reserved. i-manager Publications http://www.imanagerpublications.com/Article.aspx?ArticleId=2938