Complexity and exact values for []-Roman and strong Roman domination for specific graph families

Motivated by the original idea of defending the Roman Empire, all these domination concepts can be interpreted as vertex-labeling schemes that model the allocation of resources to protect a graph against attacks. A Roman dominating function (RDF) is a labeling of the vertices of a graph with labels...

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Autores: Valenzuela Tripodoro, Juan Carlos, Mateos Camacho, María Antonia, Cera López, Martín, Álvarez Ruiz, María del Pilar
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2026
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:dnet:idus________::f0bbeea5d4f6c7282f686bb20392be0c
Acceso en línea:https://hdl.handle.net/11441/186763
https://doi.org/10.3390/math14091535
Access Level:acceso abierto
Palabra clave:Roman domination
Triple Roman domination
Strong Roman domination
[k]-Roman domination
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spelling Complexity and exact values for []-Roman and strong Roman domination for specific graph familiesValenzuela Tripodoro, Juan CarlosMateos Camacho, María AntoniaCera López, MartínÁlvarez Ruiz, María del PilarRoman dominationTriple Roman dominationStrong Roman domination[k]-Roman dominationMotivated by the original idea of defending the Roman Empire, all these domination concepts can be interpreted as vertex-labeling schemes that model the allocation of resources to protect a graph against attacks. A Roman dominating function (RDF) is a labeling of the vertices of a graph with labels in {0,1,2} such that every vertex labeled 0 is adjacent to at least one vertex labeled 2. The weight of an RDF is the sum of all vertex labels. Vertices labeled 2 are intended to protect their neighbors labeled 0. The Roman domination number is the minimum weight of an RDF on the graph. In 2017, Álvarez et al. introduced strong Roman domination as a variant of Roman domination designed to protect the vertices of a graph against multiple simultaneous attacks. In 2021, Ahangar et al. defined [] -Roman domination, another model intended to defend a graph against individual attacks on vertices. In this paper, we investigate the computational complexity of the associated decision problems for [] -Roman domination and strong Roman domination. Furthermore, we determine exact values of these parameters for several graph families under both variants.MDPIMatemática Aplicada IFQM240: Invariantes en Teoría de Grafos y OptimizaciónMinisterio de Ciencia, Innovación y Universidades (MICIU). EspañaJunta de Andalucía2026info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/186763https://doi.org/10.3390/math14091535reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésMathematics, 14 (9), 1535. PID2022-139543OB-C41101182819FQM-240SOL2024-31708https://www.mdpi.com/2227-7390/14/9/1535info:eu-repo/semantics/openAccessoai:dnet:idus________::f0bbeea5d4f6c7282f686bb20392be0c2026-06-17T12:51:07Z
dc.title.none.fl_str_mv Complexity and exact values for []-Roman and strong Roman domination for specific graph families
title Complexity and exact values for []-Roman and strong Roman domination for specific graph families
spellingShingle Complexity and exact values for []-Roman and strong Roman domination for specific graph families
Valenzuela Tripodoro, Juan Carlos
Roman domination
Triple Roman domination
Strong Roman domination
[k]-Roman domination
title_short Complexity and exact values for []-Roman and strong Roman domination for specific graph families
title_full Complexity and exact values for []-Roman and strong Roman domination for specific graph families
title_fullStr Complexity and exact values for []-Roman and strong Roman domination for specific graph families
title_full_unstemmed Complexity and exact values for []-Roman and strong Roman domination for specific graph families
title_sort Complexity and exact values for []-Roman and strong Roman domination for specific graph families
dc.creator.none.fl_str_mv Valenzuela Tripodoro, Juan Carlos
Mateos Camacho, María Antonia
Cera López, Martín
Álvarez Ruiz, María del Pilar
author Valenzuela Tripodoro, Juan Carlos
author_facet Valenzuela Tripodoro, Juan Carlos
Mateos Camacho, María Antonia
Cera López, Martín
Álvarez Ruiz, María del Pilar
author_role author
author2 Mateos Camacho, María Antonia
Cera López, Martín
Álvarez Ruiz, María del Pilar
author2_role author
author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
FQM240: Invariantes en Teoría de Grafos y Optimización
Ministerio de Ciencia, Innovación y Universidades (MICIU). España
Junta de Andalucía
dc.subject.none.fl_str_mv Roman domination
Triple Roman domination
Strong Roman domination
[k]-Roman domination
topic Roman domination
Triple Roman domination
Strong Roman domination
[k]-Roman domination
description Motivated by the original idea of defending the Roman Empire, all these domination concepts can be interpreted as vertex-labeling schemes that model the allocation of resources to protect a graph against attacks. A Roman dominating function (RDF) is a labeling of the vertices of a graph with labels in {0,1,2} such that every vertex labeled 0 is adjacent to at least one vertex labeled 2. The weight of an RDF is the sum of all vertex labels. Vertices labeled 2 are intended to protect their neighbors labeled 0. The Roman domination number is the minimum weight of an RDF on the graph. In 2017, Álvarez et al. introduced strong Roman domination as a variant of Roman domination designed to protect the vertices of a graph against multiple simultaneous attacks. In 2021, Ahangar et al. defined [] -Roman domination, another model intended to defend a graph against individual attacks on vertices. In this paper, we investigate the computational complexity of the associated decision problems for [] -Roman domination and strong Roman domination. Furthermore, we determine exact values of these parameters for several graph families under both variants.
publishDate 2026
dc.date.none.fl_str_mv 2026
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/186763
https://doi.org/10.3390/math14091535
url https://hdl.handle.net/11441/186763
https://doi.org/10.3390/math14091535
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Mathematics, 14 (9), 1535.
PID2022-139543OB-C41
101182819
FQM-240
SOL2024-31708
https://www.mdpi.com/2227-7390/14/9/1535
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 MDPI
publisher.none.fl_str_mv MDPI
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
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