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      Permanent link:
      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

       

      S Arumugam1 2 Jay Bagga3 K Raja Chandrasekar1

      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

    • Dates

       
      Published
      November 2012
      Manuscript received
      30 March 2011
      Manuscript revised
      30 September 2011

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