Linear time algorithm for dominator chromatic number of trestled graphs-Reference-Cited by-同舟云学术

Linear time algorithm for dominator chromatic number of trestled graphs

Published:2019-12 Issue:06 Volume:11 Page:1950066
ISSN:1793-8309
Container-title:Discrete Mathematics, Algorithms and Applications
language:en
Short-container-title:Discrete Math. Algorithm. Appl.

Author:

Arumugam S.¹^ORCID,Raja Chandrasekar K.²

Affiliation:

1. National Centre for Advanced Research in Discrete Mathematics (-CARDMATH), Kalasalingam Academy of Research and Education, Anand Nagar, Krishnankoil 626126, Tamil Nadu, India

2. Department of Mathematics, Amrita College of Engineering and Technology, Amritagiri, Erachakulam Post, Nagercoil 629902, Tamil Nadu, India

Abstract

A dominator coloring (respectively, total dominator coloring) of a graph [Formula: see text] is a proper coloring [Formula: see text] of [Formula: see text] such that each closed neighborhood (respectively, open neighborhood) of every vertex of [Formula: see text] contains a color class of [Formula: see text] The minimum number of colors required for a dominator coloring (respectively, total dominator coloring) of [Formula: see text] is called the dominator chromatic number (respectively, total dominator chromatic number) of [Formula: see text] and is denoted by [Formula: see text] (respectively, [Formula: see text]). In this paper, we prove that the dominator coloring problem and the total dominator coloring problem are solvable in linear time for trestled graphs.

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793830919500666

Reference16 articles.

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2. On dominator colorings in graphs

3. Algorithmic Aspects of Dominator Colorings in Graphs

4. EQUITABLE COLORING OF 2-DEGENERATE GRAPH AND PLANE GRAPHS WITHOUT CYCLES OF SPECIFIC LENGTHS