Majority dominator colorings of graphs

TL;DR

This paper introduces the concept of majority dominator coloring in graphs, analyzing its properties, bounds, and behavior across different graph families, expanding understanding of graph coloring constraints.

Contribution

It defines the majority dominator chromatic number and establishes bounds relating it to other graph invariants, along with studying this coloring in specific graph families.

Findings

Established tight bounds for the majority dominator chromatic number.

Analyzed properties of majority dominator coloring in various graph classes.

Connected majority dominator coloring to other graph parameters like chromatic and domination numbers.

Abstract

Let $G$ be a simple graph of order $n$. A majority dominator coloring of a graph $G$ is proper coloring in which each vertex of the graph dominates at least half of one color class. The majority dominator chromatic number $\chi_{md}(G)$ is the minimum number of color classes in a majority dominator coloring of $G$. In this paper we study properties of the majority dominator coloring of a graph. We obtain tight upper and lower bounds in terms of chromatic number, dominator chromatic number, maximum degree, domination and independence number. We also study majority dominator coloring number of selected families of graphs.