IJIRST –International Journal for Innovative Research in Science & Technology| Volume 3 | Issue 12 | May 2017 ISSN (online): 2349-6010 All rights reserved by www.ijirst.org 20 The Split and Non Split Majority Domonation in Fuzzy Graphs DR. C. V. R. Harinarayanan S.Geetha Research Supervisor & Assistant Professor Assistant Professor Government Arts College, Paramakudi. Kings College of Engineering, Punalkulam. Dr.R.Muthuraj Research Supervisor & Assistant Professor H.H.The Rajah’s College(Autonomous), Pudukkottai Abstract A majority dominating set D of a fuzzy graph G is a split majority dominating set if the induced fuzzy sub graph D V  is disconnected. A majority dominating set D of a fuzzy graph G is a non- split majority dominating set if induced fuzzy sub graph D V  is connected. In this paper we study split and non-split majority domination in fuzzy graphs and its domination numbers     G and G NSM SM   .Also bounds     G and G NSM SM   with other known parameters are discussed. Keywords: Dominating set, Majority dominating set, split majority dominating set, non-split majority dominating set _______________________________________________________________________________________________________ I. INTRODUCTION A subset D V  in a fuzzy graph G is called a majority dominating set if atleast half of the vertices of of G are either in D or adjacent to the vertices of D. More clearly          2 p D N A majority dominating set D is minimal if no proper subset of D is a majority dominating set . The minimum fuzzy cardinality of a minimal majority dominating set is called the majority domination number and it is denoted by   G M  The split majority domination number   G SM  of G is the minimum fuzzy cardinality of a minimal split majority dominating set. A set D of vertices in a fuzzy graph G is dominating set if every vertex  v V is either an element of D or adjacent to an element of D. A dominating set is called minimal dominating set if no proper subset of D is a dominating set. The minimum fuzzy cardinality of a minimal dominating set is called the domination number of a fuzzy graph G and it is denoted by   G  A set D of vertices of a fuzzy graph G is said to be majority independent set if it induces a totally disconnected sub graph with   . 2 D v p D N          If any vertex D’ properly containing D is not majority independent set, then D is called maximal majority independent set. Th e maximum fuzzy cardinality of a maximal majority independent set is called majority independent number and it is denoted by   G M  Example: