Equitable Dominator Coloring of Line Graphs of Some Graphs

TL;DR

This paper investigates equitable dominator colorings, focusing on the line graphs of certain graph classes, and introduces the concept of equitable dominator chromatic number as a new coloring parameter.

Contribution

It extends the concept of equitable dominator coloring to line graphs and explores its properties for specific graph classes, introducing new theoretical insights.

Findings

Defined equitable dominator chromatic number for line graphs

Analyzed properties for specific graph classes

Established bounds and characteristics of EDCN

Abstract

A proper vertex coloring of the graph $G$ such that each vertex dominates at least one color class and the cardinalities of the color classes differ by at most $1$ is called an equitable dominator coloring of $G$. The minimum number of colors used in this coloring is called the equitable dominator chromatic number (EDCN), represented by $\chi_{ed}(G)$. This article explores the concept of equitable dominator coloring for the line graph $L(G)$ of some graph classes.