Further Results on the [k]-Roman Domination in Graphs

In 2016, Beeler et al. defined the double Roman domination as a variation of Roman domination. Sometime later, in 2021, Ahangar et al. introduced the concept of [k]- Roman domination in graphs and settled some results on the triple Roman domination case. In 2022, Amjadi et al. studied the quadruple...

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Detalhes bibliográficos
Autores: Valenzuela-Tripodoro, Juan Carlos, Mateos-Camacho, Maria Antonia, Cera López, Martín, Álvarez-Ruiz, Maria Pilar
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2024
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/170940
Acesso em linha:https://hdl.handle.net/11441/170940
https://doi.org/10.1007/s41980-024-00872-1
Access Level:acceso abierto
Palavra-chave:Roman domination
Double Roman domination
riple Roman domination
Quadruple Roman domination
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spelling Further Results on the [k]-Roman Domination in GraphsValenzuela-Tripodoro, Juan CarlosMateos-Camacho, Maria AntoniaCera López, MartínÁlvarez-Ruiz, Maria PilarRoman dominationDouble Roman dominationriple Roman dominationQuadruple Roman dominationIn 2016, Beeler et al. defined the double Roman domination as a variation of Roman domination. Sometime later, in 2021, Ahangar et al. introduced the concept of [k]- Roman domination in graphs and settled some results on the triple Roman domination case. In 2022, Amjadi et al. studied the quadruple version of this Roman-dominationtype problem. Given any labeling of the vertices of a graph, AN(v) stands for the set of neighbors of a vertex v having a positive label. In this paper we continue the study of the [k]-Roman domination functions ([k]-RDF) in graphs which coincides with the previous versions when 2 ≤ k ≤ 4. Namely, f is a [k]-RDF if f (N[v]) ≥ k+|AN(v)| for all v. We prove that the associate decision problem is NP-complete even when restricted to star convex and comb convex bipartite graphs and we also give sharp bounds and exact values for several classes of graphs.Springer NatureMatemática Aplicada I2024info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/170940https://doi.org/10.1007/s41980-024-00872-1reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésBulletin of the Iranian Mathematical Society, 50 (2), 27.https://link.springer.com/article/10.1007/s41980-024-00872-1info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1709402026-06-17T12:51:07Z
dc.title.none.fl_str_mv Further Results on the [k]-Roman Domination in Graphs
title Further Results on the [k]-Roman Domination in Graphs
spellingShingle Further Results on the [k]-Roman Domination in Graphs
Valenzuela-Tripodoro, Juan Carlos
Roman domination
Double Roman domination
riple Roman domination
Quadruple Roman domination
title_short Further Results on the [k]-Roman Domination in Graphs
title_full Further Results on the [k]-Roman Domination in Graphs
title_fullStr Further Results on the [k]-Roman Domination in Graphs
title_full_unstemmed Further Results on the [k]-Roman Domination in Graphs
title_sort Further Results on the [k]-Roman Domination in Graphs
dc.creator.none.fl_str_mv Valenzuela-Tripodoro, Juan Carlos
Mateos-Camacho, Maria Antonia
Cera López, Martín
Álvarez-Ruiz, Maria Pilar
author Valenzuela-Tripodoro, Juan Carlos
author_facet Valenzuela-Tripodoro, Juan Carlos
Mateos-Camacho, Maria Antonia
Cera López, Martín
Álvarez-Ruiz, Maria Pilar
author_role author
author2 Mateos-Camacho, Maria Antonia
Cera López, Martín
Álvarez-Ruiz, Maria Pilar
author2_role author
author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
dc.subject.none.fl_str_mv Roman domination
Double Roman domination
riple Roman domination
Quadruple Roman domination
topic Roman domination
Double Roman domination
riple Roman domination
Quadruple Roman domination
description In 2016, Beeler et al. defined the double Roman domination as a variation of Roman domination. Sometime later, in 2021, Ahangar et al. introduced the concept of [k]- Roman domination in graphs and settled some results on the triple Roman domination case. In 2022, Amjadi et al. studied the quadruple version of this Roman-dominationtype problem. Given any labeling of the vertices of a graph, AN(v) stands for the set of neighbors of a vertex v having a positive label. In this paper we continue the study of the [k]-Roman domination functions ([k]-RDF) in graphs which coincides with the previous versions when 2 ≤ k ≤ 4. Namely, f is a [k]-RDF if f (N[v]) ≥ k+|AN(v)| for all v. We prove that the associate decision problem is NP-complete even when restricted to star convex and comb convex bipartite graphs and we also give sharp bounds and exact values for several classes of graphs.
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/170940
https://doi.org/10.1007/s41980-024-00872-1
url https://hdl.handle.net/11441/170940
https://doi.org/10.1007/s41980-024-00872-1
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Bulletin of the Iranian Mathematical Society, 50 (2), 27.
https://link.springer.com/article/10.1007/s41980-024-00872-1
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer Nature
publisher.none.fl_str_mv Springer Nature
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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