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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/153215
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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 Técnicas2025-09-29T10:05:47Zoai: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:34982025-09-29 10:05:48.142CONICET 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/ |
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openAccess |
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https://creativecommons.org/licenses/by/2.5/ar/ |
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application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Open Journal Systems |
publisher.none.fl_str_mv |
Open Journal Systems |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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