$ k $-domination and total $ k $-domination numbers in catacondensed hexagonal systems

Sergio Bermudo; Robinson A. Higuita; Juan Rada; Sergio Bermudo; Robinson A. Higuita; Juan Rada

doi:10.3934/mbe.2022337

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 7: 7138-7155. doi: 10.3934/mbe.2022337

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$ k $-domination and total $ k $-domination numbers in catacondensed hexagonal systems

1.
Department of Economics, Quantitative Methods and Economic History, Pablo de Olavide University. Carretera de Utrera Km.1, 41013-Sevilla, Spain
2.
Instituto de Matemáticas, Universidad de Antioquia, Medellín, Colombia

Academic Editor: Jose M. Rodriguez

Received: 17 March 2022 Revised: 26 April 2022 Accepted: 29 April 2022 Published: 13 May 2022

In this paper we study the $ k $-domination and total $ k $-domination numbers of catacondensed hexagonal systems. More precisely, we give the value of the total domination number, we find upper and lower bounds for the $ 2 $-domination number and the total $ 2 $-domination number, characterizing the catacondensed hexagonal systems which attain these bounds, and we give the value of the $ 3 $-domination number for any catacondensed hexagonal system with a given number of hexagons. These results complete the study of $ k $-domination and total $ k $-domination of catacondensed hexagonal systems for all possible values of $ k $.
- domination,
- $ k $-domination,
- hexagonal systems,
- catacondensed hexagonal systems
Citation: Sergio Bermudo, Robinson A. Higuita, Juan Rada. $ k $-domination and total $ k $-domination numbers in catacondensed hexagonal systems[J]. Mathematical Biosciences and Engineering, 2022, 19(7): 7138-7155. doi: 10.3934/mbe.2022337

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Abstract

In this paper we study the $ k $-domination and total $ k $-domination numbers of catacondensed hexagonal systems. More precisely, we give the value of the total domination number, we find upper and lower bounds for the $ 2 $-domination number and the total $ 2 $-domination number, characterizing the catacondensed hexagonal systems which attain these bounds, and we give the value of the $ 3 $-domination number for any catacondensed hexagonal system with a given number of hexagons. These results complete the study of $ k $-domination and total $ k $-domination of catacondensed hexagonal systems for all possible values of $ k $.

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