Grundy domination and zero forcing in Kneser graphs

Autores
Bresar, Bostjan; Kos, Tim; Torres, Pablo Daniel
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we continue the investigation of different types of (Grundy) dominating sequences. We consider four different types of Grundy domination numbers and the related zero forcing numbers, focusing on these numbers in the well-known class of Kneser graphs Kn,r. In particular, we establish that the Grundy total domination number γ t gr(Kn,r) equals 2r r for any r ≥ 2 and n ≥ 2r + 1. For the Grundy domination number of Kneser graphs we get γgr(Kn,r) = α(Kn,r) whenever n is sufficiently larger than r. On the other hand, the zero forcing number Z(Kn,r) is proved to be n r − 2r r when n ≥ 3r + 1 and r ≥ 2, while lower and upper bounds are provided for Z(Kn,r) when 2r + 1 ≤ n ≤ 3r. Some lower bounds for different types of minimum ranks of Kneser graphs are also obtained along the way.
Fil: Bresar, Bostjan. University of Maribor; Eslovenia. Institute Of Mathematics, Physics And Mechanics Ljubljana; Eslovenia
Fil: Kos, Tim. Institute Of Mathematics, Physics And Mechanics Ljubljana; Eslovenia
Fil: Torres, Pablo Daniel. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Materia
GRUNDY DOMINATION NUMBER
GRUNDY TOTAL DOMINATION NUMBER
KNESER GRAPHS
ZERO FORCING NUMBER
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/153215
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Grundy domination and zero forcing in Kneser graphsBresar, BostjanKos, TimTorres, Pablo DanielGRUNDY DOMINATION NUMBERGRUNDY TOTAL DOMINATION NUMBERKNESER GRAPHSZERO FORCING NUMBERhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we continue the investigation of different types of (Grundy) dominating sequences. We consider four different types of Grundy domination numbers and the related zero forcing numbers, focusing on these numbers in the well-known class of Kneser graphs Kn,r. In particular, we establish that the Grundy total domination number γ t gr(Kn,r) equals 2r r for any r ≥ 2 and n ≥ 2r + 1. For the Grundy domination number of Kneser graphs we get γgr(Kn,r) = α(Kn,r) whenever n is sufficiently larger than r. On the other hand, the zero forcing number Z(Kn,r) is proved to be n r − 2r r when n ≥ 3r + 1 and r ≥ 2, while lower and upper bounds are provided for Z(Kn,r) when 2r + 1 ≤ n ≤ 3r. Some lower bounds for different types of minimum ranks of Kneser graphs are also obtained along the way.Fil: Bresar, Bostjan. University of Maribor; Eslovenia. Institute Of Mathematics, Physics And Mechanics Ljubljana; EsloveniaFil: Kos, Tim. Institute Of Mathematics, Physics And Mechanics Ljubljana; EsloveniaFil: Torres, Pablo Daniel. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaOpen Journal Systems2019-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/153215Bresar, Bostjan; Kos, Tim; Torres, Pablo Daniel; Grundy domination and zero forcing in Kneser graphs; Open Journal Systems; Ars Mathematica Contemporanea; 17; 2; 6-2019; 419-4301855-3966CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://amc-journal.eu/index.php/amc/article/view/1881info:eu-repo/semantics/altIdentifier/doi/10.26493/1855-3974.1881.384info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:35:31Zoai:ri.conicet.gov.ar:11336/153215instacron: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:34982025-10-22 11:35:31.967CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Grundy domination and zero forcing in Kneser graphs
title Grundy domination and zero forcing in Kneser graphs
spellingShingle Grundy domination and zero forcing in Kneser graphs
Bresar, Bostjan
GRUNDY DOMINATION NUMBER
GRUNDY TOTAL DOMINATION NUMBER
KNESER GRAPHS
ZERO FORCING NUMBER
title_short Grundy domination and zero forcing in Kneser graphs
title_full Grundy domination and zero forcing in Kneser graphs
title_fullStr Grundy domination and zero forcing in Kneser graphs
title_full_unstemmed Grundy domination and zero forcing in Kneser graphs
title_sort Grundy domination and zero forcing in Kneser graphs
dc.creator.none.fl_str_mv Bresar, Bostjan
Kos, Tim
Torres, Pablo Daniel
author Bresar, Bostjan
author_facet Bresar, Bostjan
Kos, Tim
Torres, Pablo Daniel
author_role author
author2 Kos, Tim
Torres, Pablo Daniel
author2_role author
author
dc.subject.none.fl_str_mv GRUNDY DOMINATION NUMBER
GRUNDY TOTAL DOMINATION NUMBER
KNESER GRAPHS
ZERO FORCING NUMBER
topic GRUNDY DOMINATION NUMBER
GRUNDY TOTAL DOMINATION NUMBER
KNESER GRAPHS
ZERO FORCING NUMBER
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 continue the investigation of different types of (Grundy) dominating sequences. We consider four different types of Grundy domination numbers and the related zero forcing numbers, focusing on these numbers in the well-known class of Kneser graphs Kn,r. In particular, we establish that the Grundy total domination number γ t gr(Kn,r) equals 2r r for any r ≥ 2 and n ≥ 2r + 1. For the Grundy domination number of Kneser graphs we get γgr(Kn,r) = α(Kn,r) whenever n is sufficiently larger than r. On the other hand, the zero forcing number Z(Kn,r) is proved to be n r − 2r r when n ≥ 3r + 1 and r ≥ 2, while lower and upper bounds are provided for Z(Kn,r) when 2r + 1 ≤ n ≤ 3r. Some lower bounds for different types of minimum ranks of Kneser graphs are also obtained along the way.
Fil: Bresar, Bostjan. University of Maribor; Eslovenia. Institute Of Mathematics, Physics And Mechanics Ljubljana; Eslovenia
Fil: Kos, Tim. Institute Of Mathematics, Physics And Mechanics Ljubljana; Eslovenia
Fil: Torres, Pablo Daniel. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
description In this paper, we continue the investigation of different types of (Grundy) dominating sequences. We consider four different types of Grundy domination numbers and the related zero forcing numbers, focusing on these numbers in the well-known class of Kneser graphs Kn,r. In particular, we establish that the Grundy total domination number γ t gr(Kn,r) equals 2r r for any r ≥ 2 and n ≥ 2r + 1. For the Grundy domination number of Kneser graphs we get γgr(Kn,r) = α(Kn,r) whenever n is sufficiently larger than r. On the other hand, the zero forcing number Z(Kn,r) is proved to be n r − 2r r when n ≥ 3r + 1 and r ≥ 2, while lower and upper bounds are provided for Z(Kn,r) when 2r + 1 ≤ n ≤ 3r. Some lower bounds for different types of minimum ranks of Kneser graphs are also obtained along the way.
publishDate 2019
dc.date.none.fl_str_mv 2019-06
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/11336/153215
Bresar, Bostjan; Kos, Tim; Torres, Pablo Daniel; Grundy domination and zero forcing in Kneser graphs; Open Journal Systems; Ars Mathematica Contemporanea; 17; 2; 6-2019; 419-430
1855-3966
CONICET Digital
CONICET
url http://hdl.handle.net/11336/153215
identifier_str_mv Bresar, Bostjan; Kos, Tim; Torres, Pablo Daniel; Grundy domination and zero forcing in Kneser graphs; Open Journal Systems; Ars Mathematica Contemporanea; 17; 2; 6-2019; 419-430
1855-3966
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://amc-journal.eu/index.php/amc/article/view/1881
info:eu-repo/semantics/altIdentifier/doi/10.26493/1855-3974.1881.384
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Open Journal Systems
publisher.none.fl_str_mv Open Journal Systems
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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