Rangarajan, R. and Kalarkop, David. A.
(2022)
*A note on global dominator coloring of graphs.*
Discrete Mathematics, Algorithms and Applications, 14 (05).
p. 2150158.
ISSN 1793-8317

## Abstract

Global dominator coloring of the graph G is the proper coloring of G such that every vertex of G dominates atleast one color class as well as anti-dominates atleast one color class. The minimum number of colors required for global dominator coloring of G is called global dominator chromatic number of G denoted by Ï‡gd(G). In this paper, we characterize trees T of order n (n â‰¥ 6) such that Ï‡gd(T) = âŒŠn 2 âŒ‹ + 2 and also establish a strict upper bound for Ï‡gd(T) for a tree of even order n (n â‰¥ 6). We construct some family of graphs G with Ï‡gd(G) = 4 and prove some results on Ï‡gd-partitions of G when Ï‡gd(G) = 4.

Item Type: | Article |
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Subjects: | E Mathematical Science > Mathematics |

Divisions: | Department of > Mathematics |

Depositing User: | C Swapna Library Assistant |

Date Deposited: | 14 Jun 2023 06:04 |

Last Modified: | 14 Jun 2023 06:04 |

URI: | http://eprints.uni-mysore.ac.in/id/eprint/17523 |

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