On inertia and ratio type bounds for the k-independence number of a graph and their relationship

© 2023 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Detalles Bibliográficos
Autores: Abiad, Aida, Dalfó Simó, Cristina|||0000-0002-8438-9353, Fiol Mora, Miquel Àngel|||0000-0003-1337-4952, Zeijlemaker, Sjanne
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/393526
Acceso en línea:https://hdl.handle.net/2117/393526
https://dx.doi.org/10.1016/j.dam.2023.03.015
Access Level:acceso abierto
Palabra clave:Graph theory
k-power graph
Independence number
Adjacency spectrum
Polynomialsk-partially walk-regular
Mixed integer linear programming
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
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network_name_str España
repository_id_str
spelling On inertia and ratio type bounds for the k-independence number of a graph and their relationshipAbiad, AidaDalfó Simó, Cristina|||0000-0002-8438-9353Fiol Mora, Miquel Àngel|||0000-0003-1337-4952Zeijlemaker, SjanneGraph theoryk-power graphIndependence numberAdjacency spectrumPolynomialsk-partially walk-regularMixed integer linear programmingGrafs, Teoria deClassificació AMS::05 Combinatorics::05C Graph theoryÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs© 2023 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/For , the -independence number of a graph is the maximum number of vertices that are mutually at distance greater than . The well-known inertia and ratio bounds for the (1-)independence number of a graph, due to Cvetković and Hoffman, respectively, were generalized recently for every value of . We show that, for graphs with enough regularity, the polynomials involved in such generalizations are closely related and give exact values for , showing a new relationship between the inertia and ratio type bounds. Additionally, we investigate the existence and properties of the extremal case of sets of vertices that are mutually at maximum distance for walk-regular graphs. Finally, we obtain new sharp inertia and ratio type bounds for partially walk-regular graphs by using the predistance polynomials.The research of Aida Abiad is partially supported by the FWO, Belgium grant 1285921N. The research of Cristina Dalfó and Miquel Àngel Fiol has been partially supported by AGAUR from the Catalan Government under project 2021SGR00434 and MICINN from the Spanish Government under project PID2020-115442RB-I00.Peer ReviewedElsevier20232023-07-1520232023-09-15journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/393526https://dx.doi.org/10.1016/j.dam.2023.03.015reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttps://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3935262026-05-27T15:37:01Z
dc.title.none.fl_str_mv On inertia and ratio type bounds for the k-independence number of a graph and their relationship
title On inertia and ratio type bounds for the k-independence number of a graph and their relationship
spellingShingle On inertia and ratio type bounds for the k-independence number of a graph and their relationship
Abiad, Aida
Graph theory
k-power graph
Independence number
Adjacency spectrum
Polynomialsk-partially walk-regular
Mixed integer linear programming
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
title_short On inertia and ratio type bounds for the k-independence number of a graph and their relationship
title_full On inertia and ratio type bounds for the k-independence number of a graph and their relationship
title_fullStr On inertia and ratio type bounds for the k-independence number of a graph and their relationship
title_full_unstemmed On inertia and ratio type bounds for the k-independence number of a graph and their relationship
title_sort On inertia and ratio type bounds for the k-independence number of a graph and their relationship
dc.creator.none.fl_str_mv Abiad, Aida
Dalfó Simó, Cristina|||0000-0002-8438-9353
Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
Zeijlemaker, Sjanne
author Abiad, Aida
author_facet Abiad, Aida
Dalfó Simó, Cristina|||0000-0002-8438-9353
Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
Zeijlemaker, Sjanne
author_role author
author2 Dalfó Simó, Cristina|||0000-0002-8438-9353
Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
Zeijlemaker, Sjanne
author2_role author
author
author
dc.subject.none.fl_str_mv Graph theory
k-power graph
Independence number
Adjacency spectrum
Polynomialsk-partially walk-regular
Mixed integer linear programming
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
topic Graph theory
k-power graph
Independence number
Adjacency spectrum
Polynomialsk-partially walk-regular
Mixed integer linear programming
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
description © 2023 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-07-15
2023
2023-09-15
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/393526
https://dx.doi.org/10.1016/j.dam.2023.03.015
url https://hdl.handle.net/2117/393526
https://dx.doi.org/10.1016/j.dam.2023.03.015
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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