Tight Just Chromatic Excellence In Fuzzy Graphs

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R.Udaya Suriya, K. M. D. (2017). Tight Just Chromatic Excellence In Fuzzy Graphs. Asian Journal of Current Engineering and Maths, 6(3), 31–34. https://doi.org/10.15520/ajcem.2017.vol6.iss3.78.pp31-34.
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Abstract

Let G be a simple fuzzy graph. A family   Γᶠ = { γ1, γ2,…, γk}  of  fuzzy sets on a set V  is called k-fuzzy colouring of  V = (V,σ,µ)  if  i) ∪ Γᶠ = σ,  ii) γi∩ γj = Ф, iii) for every strong edge (x,y) (i.e., µ(xy) > 0) of  G  min{γi(x), γj(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 χf (G). Then Γᶠ  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 χf -excellent if every vertex of G appears as a singleton in exactly one _f -partition of G. A just χf –excellent graph of order n is called the tight just χf -excellent if G having exactly n, χf -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 χf -excellent, fuzzy colourful vertex, fuzzy kneser graph.

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