• On Dominator Colorings in Graphs

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/122/04/0561-0571

• # Keywords

Dominator coloring; dominator chromatic number; chromatic number; domination number.

• # Abstract

A dominator coloring of a graph 𝐺 is a proper coloring of 𝐺 in which every vertex dominates every vertex of at least one color class. The minimum number of colors required for a dominator coloring of 𝐺 is called the dominator chromatic number of 𝐺 and is denoted by $\chi d(G)$. In this paper we present several results on graphs with $\chi d(G)=\chi(G)$ and $\chi d(G)=\gamma(G)$ where $\chi(G)$ and $\gamma(G)$ denote respectively the chromatic number and the domination number of a graph 𝐺. We also prove that if $\mu(G)$ is the Mycielskian of 𝐺, then $\chi d(G)+1\leq\chi d(\mu(G))\leq\chi d(G)+2$.

• # Author Affiliations

1. National Centre for Advanced Research in Discrete Mathematics (𝑛-CARDMATH), Kalasalingam University, Anand Nagar, Krishnankoil 626126, India
2. School of Electrical Engineering and Computer Science, The University of Newcastle, Newcastle, NSW 2308, Australia
3. Department of Computer Science, Ball State University, Muncie, IN 47306, USA

• # Proceedings – Mathematical Sciences

Volume 132, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019

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