International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 05 Issue: 05 | May-2018 www.irjet.net p-ISSN: 2395-0072 © 2018, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 4041 STRONG INVERSE SPLIT AND NON-SPLIT DOMINATION IN JUMP GRAPHS N.Pratap Babu Rao Department of Mathematics S.G.degree College koppal (Karnataka)INDIA ------------------------------------------------------------------------------***------------------------------------------------------------------------------- Abstract : In this paper strong inverse split , non- split dominating sets are introduced and its properties are studied. Further the notion of strong co-edge split, non-split domination sets are discussed. Key Words; Strong(weak)inverse split domination set, Strong(weak) inverse non-split domination set Strong (weak) co-edge split domination set Strong (weak) co-edge non-split dominating set. 2010. Ams subject Classification 05C69 1. Introduction: In 1958, domination as a theoretical area in graph then was formalized by Berge and Ore [2] in 1962. Let G=(V, E) be a graph. A set D  V is a strong dominating set of G if for every vertex y  V-D there exists x  D with xy  E of larger or equal degree that is deg (X, G) ≤ d(x,G). The strong dominate number √st(G) is defined as the minimum cardinality of a strong dominating set and was introduced by Sampathkumar and Puspalata[1] in 1996.Kulli V.R and Janakiram B [ 6, 5] was introduced split dominating and non-split domination number was introduced . In 2010 K.Ameenal Bibi and R. Selvakumar [4] was introduced the inverse split and non-split dominating sets are introduced and properties are discussed. We also introduced the notation of Co-edge split and non-split domination sets in jump graphs and study its properties. 2.Preliminaries: Definition 2.1 [3] A graph G is an ordered triple ( V,E, Ѱ )consisting of a nonempty set V(G) of vertices a set E(G) of edges, disjoint from V(G) of edges and incident function Ѱ that associates with each edge of G an unordered pair of vertices of G. If e is an edge and u and v are vertices such that Ѱ(e)=uv there is said to join u and v. The vertices u and v are called ends of e. Definition 2.2[2] A vertex v in a graph G is said to be dominate itself and each of its neighbors that is v dominates the vertices in its closed neighborhood N[v]. a set S of vertices of G is a dominating set of G if every vertex of G dominated by atleast one vertex of S. Equivalently a set S of vertices of G is a dominating set of every vertex in V-S is adjacent to at least one vertex in S. The minimum cardinality among the dominating setoff g is called dominating number and is denoted by √(G). a dominating set of cardinality of √(G) is then referred to as minimum dominating set. Definition 2.3[1] A set D  V is a dominating set (strong dominating set sd-set), weak dominating set (wd-set of G if every v  V-D is dominated (strongly dominating , weakly dominating respectively) by some vertex u  D. The domination number sd, wd number) √ = √(G) ( √s= √s(G), √w = √w(G) ) of G is the minimum cardinality of a dominating set (sd-set, wd- set) of G. Definition 2.4 A set D  V is a dominating set (strong dominating set sd-set), weak dominating set (wd-set of jump gaph J( G) if every v  V-D is dominated (strongly dominating , weakly dominating respectively) by some vertex u  D. The domination number sd, wd number) √ = √(J(G)) ( √s= √s(J(G)), √w = √w(J(G) ) of jump graph J(G) is the minimum