JUST CHROMATIC EXCELLENCE IN FUZZY GRAPHS

Abstract

Abstaract−Let G be a simple fuzzy graph. A family Γf= {γ, 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= ∅, iii)for every strong edge (x, y)(i.e., µ(xy) > 0) of G min{γi(x), γi(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 Γfis 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 χf-partition of G. This paper aims at the study of the new concept namely Just Chromatic excellence in fuzzy graphs. Fuzzy colourful vertex is defined and studied. We explain these new concepts through examples

Keywords

• −fuzzy chromatic excellent, fuzzy just excellent,fuzzy colourful vertex

JUST CHROMATIC EXCELLENCE IN FUZZY GRAPHS

Abstract