Grundy dominating sequences on X-join product
- Autores
- Nasini, Graciela Leonor; Torres, Pablo
- Año de publicación
- 2020
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this paper we study the Grundy domination number on the X-join product G↩R of a graph G and a family of graphs R={Gv:v∈V(G)}. The results led us to extend the few known families of graphs where this parameter can be efficiently computed. We prove that if, for all v∈V(G), the Grundy domination number of Gv is given, and G is a power of a cycle, a power of a path, or a split graph, computing the Grundy domination number of G↩R can be done in polynomial time. In particular, our results for powers of cycles and paths are derived from a polynomial reduction to the Maximum Weight Independent Set problem on these graphs. As a consequence, we derive closed formulas to compute the Grundy domination number of the lexicographic product G∘H when G is a power of a cycle, a power of a path or a split graph, generalizing the results on cycles and paths given by Brešar et al. in 2016. Moreover, our results on the X-join product when G is a split graph also provide polynomial-time algorithms to compute the Grundy domination number for (q,q−4) graphs, partner limited graphs and extended P4-laden graphs, graph classes that are high in the hierarchy of few P4’s graphs.
Fil: Nasini, Graciela Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Torres, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina - Materia
-
GRUNDY DOMINATING SEQUENCES
POWERS OF CYCLES
POWERS OF PATHS
SPLIT GRAPHS
X-JOIN PRODUCT - Nivel de accesibilidad
- acceso embargado
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/114077
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Grundy dominating sequences on X-join productNasini, Graciela LeonorTorres, PabloGRUNDY DOMINATING SEQUENCESPOWERS OF CYCLESPOWERS OF PATHSSPLIT GRAPHSX-JOIN PRODUCThttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we study the Grundy domination number on the X-join product G↩R of a graph G and a family of graphs R={Gv:v∈V(G)}. The results led us to extend the few known families of graphs where this parameter can be efficiently computed. We prove that if, for all v∈V(G), the Grundy domination number of Gv is given, and G is a power of a cycle, a power of a path, or a split graph, computing the Grundy domination number of G↩R can be done in polynomial time. In particular, our results for powers of cycles and paths are derived from a polynomial reduction to the Maximum Weight Independent Set problem on these graphs. As a consequence, we derive closed formulas to compute the Grundy domination number of the lexicographic product G∘H when G is a power of a cycle, a power of a path or a split graph, generalizing the results on cycles and paths given by Brešar et al. in 2016. Moreover, our results on the X-join product when G is a split graph also provide polynomial-time algorithms to compute the Grundy domination number for (q,q−4) graphs, partner limited graphs and extended P4-laden graphs, graph classes that are high in the hierarchy of few P4’s graphs.Fil: Nasini, Graciela Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Torres, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaElsevier Science2020-09info:eu-repo/date/embargoEnd/2021-03-31info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/114077Nasini, Graciela Leonor; Torres, Pablo; Grundy dominating sequences on X-join product; Elsevier Science; Discrete Applied Mathematics; 284; 9-2020; 138-1490166-218XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1810.02737info:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2020.03.016info:eu-repo/semantics/embargoedAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:07:26Zoai:ri.conicet.gov.ar:11336/114077instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:07:27.174CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Grundy dominating sequences on X-join product |
title |
Grundy dominating sequences on X-join product |
spellingShingle |
Grundy dominating sequences on X-join product Nasini, Graciela Leonor GRUNDY DOMINATING SEQUENCES POWERS OF CYCLES POWERS OF PATHS SPLIT GRAPHS X-JOIN PRODUCT |
title_short |
Grundy dominating sequences on X-join product |
title_full |
Grundy dominating sequences on X-join product |
title_fullStr |
Grundy dominating sequences on X-join product |
title_full_unstemmed |
Grundy dominating sequences on X-join product |
title_sort |
Grundy dominating sequences on X-join product |
dc.creator.none.fl_str_mv |
Nasini, Graciela Leonor Torres, Pablo |
author |
Nasini, Graciela Leonor |
author_facet |
Nasini, Graciela Leonor Torres, Pablo |
author_role |
author |
author2 |
Torres, Pablo |
author2_role |
author |
dc.subject.none.fl_str_mv |
GRUNDY DOMINATING SEQUENCES POWERS OF CYCLES POWERS OF PATHS SPLIT GRAPHS X-JOIN PRODUCT |
topic |
GRUNDY DOMINATING SEQUENCES POWERS OF CYCLES POWERS OF PATHS SPLIT GRAPHS X-JOIN PRODUCT |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
In this paper we study the Grundy domination number on the X-join product G↩R of a graph G and a family of graphs R={Gv:v∈V(G)}. The results led us to extend the few known families of graphs where this parameter can be efficiently computed. We prove that if, for all v∈V(G), the Grundy domination number of Gv is given, and G is a power of a cycle, a power of a path, or a split graph, computing the Grundy domination number of G↩R can be done in polynomial time. In particular, our results for powers of cycles and paths are derived from a polynomial reduction to the Maximum Weight Independent Set problem on these graphs. As a consequence, we derive closed formulas to compute the Grundy domination number of the lexicographic product G∘H when G is a power of a cycle, a power of a path or a split graph, generalizing the results on cycles and paths given by Brešar et al. in 2016. Moreover, our results on the X-join product when G is a split graph also provide polynomial-time algorithms to compute the Grundy domination number for (q,q−4) graphs, partner limited graphs and extended P4-laden graphs, graph classes that are high in the hierarchy of few P4’s graphs. Fil: Nasini, Graciela Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina Fil: Torres, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina |
description |
In this paper we study the Grundy domination number on the X-join product G↩R of a graph G and a family of graphs R={Gv:v∈V(G)}. The results led us to extend the few known families of graphs where this parameter can be efficiently computed. We prove that if, for all v∈V(G), the Grundy domination number of Gv is given, and G is a power of a cycle, a power of a path, or a split graph, computing the Grundy domination number of G↩R can be done in polynomial time. In particular, our results for powers of cycles and paths are derived from a polynomial reduction to the Maximum Weight Independent Set problem on these graphs. As a consequence, we derive closed formulas to compute the Grundy domination number of the lexicographic product G∘H when G is a power of a cycle, a power of a path or a split graph, generalizing the results on cycles and paths given by Brešar et al. in 2016. Moreover, our results on the X-join product when G is a split graph also provide polynomial-time algorithms to compute the Grundy domination number for (q,q−4) graphs, partner limited graphs and extended P4-laden graphs, graph classes that are high in the hierarchy of few P4’s graphs. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-09 info:eu-repo/date/embargoEnd/2021-03-31 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/114077 Nasini, Graciela Leonor; Torres, Pablo; Grundy dominating sequences on X-join product; Elsevier Science; Discrete Applied Mathematics; 284; 9-2020; 138-149 0166-218X CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/114077 |
identifier_str_mv |
Nasini, Graciela Leonor; Torres, Pablo; Grundy dominating sequences on X-join product; Elsevier Science; Discrete Applied Mathematics; 284; 9-2020; 138-149 0166-218X CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1810.02737 info:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2020.03.016 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/embargoedAccess https://creativecommons.org/licenses/by-nc-nd/2.5/ar/ |
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embargoedAccess |
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https://creativecommons.org/licenses/by-nc-nd/2.5/ar/ |
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application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier Science |
publisher.none.fl_str_mv |
Elsevier Science |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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