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Total Global Dominator Coloring of Trees and Unicyclic Graphs

Authors

  • Chithra K. P. Department of Mathematics, Christ University, Bangalore-560029, Karnataka, INDIA. https://orcid.org/0000-0003-3871-1345
  • Joseph Mayamma Department of Mathematics, Christ University, Bangalore-560029, Karnataka, INDIA.

DOI:

https://doi.org/10.21123/bsj.2023.6457

Keywords:

Global dominator coloring, Total domination number, Total dominator coloring, Total global domination number, Total global dominator coloring, Trees, Unicyclic graphs. MSC2020: 05C15, 05C69

Abstract

          A total global dominator coloring of a graph  is a proper vertex coloring of  with respect to which every vertex  in  dominates a color class, not containing  and does not dominate another color class. The minimum number of colors required in such a coloring of  is called the total global dominator chromatic number, denoted by . In this paper, the total global dominator chromatic number of trees and unicyclic graphs are explored.

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