S.Geetha Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 4, Issue 6( Version 2), June 2014, pp.118-121 www.ijera.com 118 | Page Inverse Split and Non split Domination in Fuzzy graphs S.Geetha *, C.V.R.Harinarayanan ** *(Department of Mathematics, Kings College of Engineering, Punalkulam) ** (Department of Mathematics, the Govt. Arts. College, Paramakudi) ABSTRACT In this paper we define the notions of inverse split and non split domination in fuzzy graphs. We get many bounds on inverse split and non split domination numbers. Keywords – dominating set, split dominating set, inverse split dominating set, non split dominating set, inverse non split dominating set. I. INTRODUCTION Rosenfeld introduced the concept of fuzzy graph and several fuzzy analogs of graph theoretic concepts such as paths, cycles and connectedness.Nagoorgani and Chandrasekaran discussed domination in fuzzy graph using strong arcs.Kulli V.R introduced the concept of split domination and non split domination in graphs. This paper deals with inverse split and non-split domination in fuzzy graphs Definition: 1.1 A non empty set V D  of a fuzzy graph     ,  G is a dominating set of G if every vertex in V-D is adjacent to some vertex in D.The domination number   G  is the minimum cardinality taken over all the minimal dominating sets of G. Definition: 1.2 Let D be the minimum dominating set of G.If V-D contains a dominating set ' D then ' D is called the inverse dominating set of G with respect to D.The inverse domination number   G '  is the minimum cardinality taken over all the minimal inverse dominating set of G. Definition: 13 A dominating set of a fuzzy graph G is a split (non split) dominating set if the induced subgraph D V  is disconnected (connected). Definition: 1.4 The split (non split) domination number       G G ns s   is the minimum cardinality of a split(non split) dominating set. Definition: 1.5 Two nodes that are joined by a path are said to be connected. II MAIN RESULTS Definition: 2.1 Let ' D be the minimum inverse dominating set of G with respect to D.Then ' D is called an inverse split(non split )dominating set of G if the induced subgraph is D V '  disconnected(connected). The inverse split (non-split) domination number is denoted by     G G ns s ' ' ) (   and is the minimum cardinality taken over all the minimal inverse split (non-split)dominating sets of G.Bounds on     G and G ns s ' '   are also obtained. Remark: i)For any complete fuzzy graph n K with 2  n vertices     1 0 ' '   n ns n s K and K   ii)   0 '  n ns C  EXAMPLE: 2.2 RESEARCH ARTICLE OPEN ACCESS