JUST CHROMATIC EXCELLENCE IN ANTI-FUZZY GRAPHS

摘要

Let G be a simple anti-fuzzy graph (AFG). A family C = {c_1,…,c_k} of anti-fuzzy sets on a set V is called a kvertex coloring of G = (V,σ,μ)if (i) ∨ c_i(x) = σ(x), for all x ∈ V,(ii) c)_i ∧c_j = 0,(iii) For every strong edge xy of G, min {c_i(σ(x)), {c_i(σ(y))}=0,(1 ≤ i ≤ k). The least value of k for which the G has a k-vertex coloring denoted by χ(G), is called the chromatic number of the anti-fuzzy graph G. Then C is the partition of independent sets of vertices of G in which each set has the same color is called the chromatic partition. An anti-fuzzy graph G is called the just χ-excellent if every vertex of G appears as a singleton in exactly one χ-partitions of G. A just χ- excellent graph of order n is called the tight just χ-excellent graph if G having exactly n, χ-partition.The focal point of this paper is to study the new concept called just chromatic excellence and tight just chromatic excellence in anti-fuzzy graphs. We explain these new concepts through illustrative examples.