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

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Titel: $ k $-domination and total $ k $-domination numbers in catacondensed hexagonal systems
Autoren: Sergio Bermudo, Robinson A. Higuita, Juan Rada
Quelle: Mathematical Biosciences and Engineering, Vol 19, Iss 7, Pp 7138-7155 (2022)
Verlagsinformationen: American Institute of Mathematical Sciences (AIMS), 2022.
Publikationsjahr: 2022
Schlagwörter: hexagonal systems, Constraint Satisfaction Problems, Domination analysis, 0102 computer and information sciences, Mathematical analysis, 01 natural sciences, Graph, Upper and lower bounds, Value (mathematics), 0103 physical sciences, QA1-939, FOS: Mathematics, domination, catacondensed hexagonal systems, Crystallography, Hexagonal crystal system, Graph Spectra and Topological Indices, Statistics, k-domination, Vertex (graph theory), Chemistry, Topological Data Analysis in Science and Engineering, Computational Theory and Mathematics, Combinatorics, Physical Sciences, Computer Science, Geometry and Topology, TP248.13-248.65, Mathematics, Biotechnology, Graph Theory and Algorithms
Beschreibung: 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 $.
Publikationsart: Article
Other literature type
ISSN: 1551-0018
DOI: 10.3934/mbe.2022337
DOI: 10.60692/peqz5-rwc48
DOI: 10.60692/vz4rg-ywk83
Zugangs-URL: https://pubmed.ncbi.nlm.nih.gov/35730300
https://doaj.org/article/6f20c38a6a98424399bd24f84fe541ff
Dokumentencode: edsair.doi.dedup.....c9813c39a2c9fc24a28e82ed1a2fa88e
Datenbank: OpenAIRE
Beschreibung
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 $.
ISSN:15510018
DOI:10.3934/mbe.2022337