1Research Scholar, P.G. and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli, Tamil Nadu620020, India
2Assistant Professor, P.G. and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli, Tamil Nadu620020, India
3Principal and Head, P.G. and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli, Tamil Nadu620020, India
*Corresponding Author: M.A. Rifayathali, Research Scholar, PG and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli, Tamil Nadu 620020, India. E-mail: rifayathali.maths@gmail.com
**E-mail: apj_jmc@yahoo.co.in
***E-mail: simohideen@yahoo.co.in
Let G be a simple anti-fuzzy graph (AFG). A family C = {c1,…, ck} of anti-fuzzy sets on a set V is called a k-vertex coloring of G = (V,σ,μ) if
˅ ci(x) = σ(x), for all x ∈ V,
ci ∧ ci = 0,
For every strong edge xy of G, min{ci(σ(x)),ci(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.
Antifuzzy graph, Chromatic excellence, Justchromatic excellence, Tight just chromatic excellence, 05C72, 05C15
