Some New Results on Equitable Dominator Coloring of Graphs

An equitable dominator coloring is 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 $1$. The minimum number of colors used in this coloring is called the equitable dominator chromatic number, represented by $\chi_{ed}(G)$. This article explores the concept of equitable dominator coloring of some graph operations, such as join of graphs, cartesian products, and tensor products of graphs.