JUST CHROMATIC EXCELLENCE IN ANTI-FUZZY GRAPHS

M A Rifayathali; A Prasanna; S Ismail Mohideen

doi:10.48165/

Authors

M A Rifayathali Research Scholar, P.G. and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli, Tamil Nadu 620020, India.
A Prasanna Assistant Professor, P.G. and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli, Tamil Nadu 620020, India.
S Ismail Mohideen Principal and Head, P.G. and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli, Tamil Nadu 620020, India.

DOI:

https://doi.org/10.48165/

Keywords:

Antifuzzy graph, Chromatic excellence, Justchromatic excellence, Tight just chromatic excellence

Abstract

Let   be a simple anti-fuzzy graph (AFG). A family   = , … ,   of anti-fuzzy sets on a set V is called a k vertex coloring of   =
, , if (i) ∨
=
, for all   ∈ , (ii)    ∧   = 0, (iii) For every strong edge    of , min ,
= 0,
1 ≤ " ≤ # . The least value of k for which the   has a k-vertex coloring denoted by %
, is called the chromatic number of the anti-fuzzy graph . Then   is the partition of independent sets of vertices of   in which each set has the same color is called the chromatic partition. An anti-fuzzy graph   is called the just %-excellent if every vertex of   appears as a singleton in exactly one %-partitions of . A just %- excellent graph of order n is called the tight just %-excellent graph if G having exactly n, %-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.

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