Non Split Domination on Intuitionistic Fuzzy Graphs

A dominating set D of an IFG G = (V, E) is a non-split dominating set, if the induced intuitionistic fuzzy subgraph 〈ܸ − ‫〉ܦ‬ is connected. The Non-split domination number ߛ ௡௦ ሺ‫ܩ‬ሻ of IFG G is the minimum cardinality of all Non-split dominating set. In this paper we study some theorems in Non-split dominating sets of IFG and some results of ߛ ௡௦ ሺ‫ܩ‬ሻwith other known parameters of IFG G. 1. Introduction In 1965, the notion of fuzzy sets was introduced by Zadeh [21] as a method of representing uncertainty and vagueness. In 1986, Atanassov [1] introduced the concept of IF sets as a generalization of fuzzy sets. The fuzzy relations between fuzzy sets were concluded by Rosenfeld and he developed the structure of fuzzy graphs, obtaining analogs of several graph theoretical concepts. Bhattacharya [3] gave some remarks on fuzzy graphs and some operations on fuzzy graphs were included by Mordeson and Peng [8]. Kulli [7] wrote on theory of domination in graphs. Cockayne [5] introduced the independent domination number in graphs. Somasundaram and Somasundaram [19] presentedmore concepts of independent domination, connected domination in fuzzy graphs. Parvathi and Karunambigai [15] gave a definition of IFG as a special case of IFGS defined by Atanassov and Shannon [18]. Nagoor Gani and Begum [12] gave the definition of order, degree and size in IFG. Later Parvathi and Thamizhendhi [16] introduced dominating set, domination number, independent set, total dominating set and total domination number in IFGs. In this Paper, non-split dominating sets in IFGs are studied.