Equitable Associate Fuzzy Graph of a Fuzzy Graph


M. Rani - Department of Mathematics, Madurai Kamaraj University College Aundipatti,Tamilnadu State, India. K. M. Dharmalingam - Department of Mathematics, The Madura College Madurai, Tamilnadu State, India.


Let \(G= (V, \sigma, \mu)\) be a fuzzy graph. Let \(H\) be the graph constructed from \(G\) as follows \(V(H) =V(G)\), two points \(u\) and \(v\) are adjacent in \(H\) if and only if \(u\) and \(v\) are adjacent and degree fuzzy equitable in \(G\). \(H\) is called the adjacency inherent fuzzy equitable graph of \(G\) or fuzzy equitable associate graph of \(G\) and is denoted by \(e^{ef}(G)\). In this paper we introduced the concept of fuzzy equitable associate graph and obtain some interesting results for this new parameter in fuzzy equitable associate graph.