Equitable Dominator Coloring of Line Graphs of Some Graphs

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.