Tight Just Chromatic Excellence In Fuzzy Graphs

Abstract

Let G be a simple fuzzy graph. A family   I“a¶  = { I³1, I³2,…, I³k}  of  fuzzy sets on a set V  is called k-fuzzy colouring of  V = (V,Iƒ,µ)  if  i) âˆa I“a¶  = Iƒ,  ii) I³i∩ I³j = Ф, iii) for every strong edge (x,y) (i.e., µ(xy) > 0) of  G  min{I³i(x), I³j(y)} = 0; (1 ≤ i ≤ k). The minimum number of  k for which there exists a k-fuzzy colouring is called the fuzzy chromatic number of G denoted as I‡f (G). Then I“a¶   is the partition of independent sets of vertices of  G  in which each sets has the same colour is called the fuzzy chromatic partition. A graph G is called the just I‡f -excellent if every vertex of G appears as a singleton in exactly one _f -partition of G. A just I‡f –excellent graph of order n is called the tight just I‡f -excellent if G having exactly n, I‡f -partitions. This paper aims at the study of the new concept namely tight just Chromatic excellence in fuzzy graphs and its properties. 02000 Mathematics Subject Classification:05C72 Key words: fuzzy just chromatic excellent, tight just I‡f -excellent, fuzzy colourful vertex, fuzzy kneser graph.