Doubling constants and spectral theory on graphs

We study the least doubling constant among all possible doubling measures defined on a (finite or infinite) graph G. We show that this constant can be estimated from below by 1 + r(AG ), where r(AG ) is the spectral radius of the adjacency matrix of G, and study when both quantities coincide. We als...

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Detalles Bibliográficos
Autores: Durand-Cartagena, Estibalitz, Soria de Diego, Francisco Javier, Tradacete Pérez, Pedro
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/105183
Acceso en línea:https://hdl.handle.net/20.500.14352/105183
Access Level:acceso abierto
Palabra clave:Doubling measure
Infinite graph
Spectral graph theory
Matemáticas (Matemáticas)
12 Matemáticas
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spelling Doubling constants and spectral theory on graphsDurand-Cartagena, EstibalitzSoria de Diego, Francisco JavierTradacete Pérez, PedroDoubling measureInfinite graphSpectral graph theoryMatemáticas (Matemáticas)12 MatemáticasWe study the least doubling constant among all possible doubling measures defined on a (finite or infinite) graph G. We show that this constant can be estimated from below by 1 + r(AG ), where r(AG ) is the spectral radius of the adjacency matrix of G, and study when both quantities coincide. We also illustrate how amenability of the automorphism group of a graph can be related to finding doubling minimizers. Finally, we give a complete characterization of graphs with doubling constant smaller than 3, in the spirit of Smith graphs.ElsevierUniversidad Complutense de Madrid20232023-01-0120232023-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/105183reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PGC2018-097286-B-I00 ANALISIS FUNCIONAL NO LINEAL Y GEOMETRICOAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113048GB-I00 ESPACIOS DE FUNCIONES Y TECNICAS DE ACOTACION DE OPERADORES EN ANALISISAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-116398GB-I00 APLICACIONES DEL ANALISIS FUNCIONAL EN PROBLEMAS DE GEOMETRIA Y TEORIA DE LA INFORMACIONopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/1051832026-06-02T12:44:21Z
dc.title.none.fl_str_mv Doubling constants and spectral theory on graphs
title Doubling constants and spectral theory on graphs
spellingShingle Doubling constants and spectral theory on graphs
Durand-Cartagena, Estibalitz
Doubling measure
Infinite graph
Spectral graph theory
Matemáticas (Matemáticas)
12 Matemáticas
title_short Doubling constants and spectral theory on graphs
title_full Doubling constants and spectral theory on graphs
title_fullStr Doubling constants and spectral theory on graphs
title_full_unstemmed Doubling constants and spectral theory on graphs
title_sort Doubling constants and spectral theory on graphs
dc.creator.none.fl_str_mv Durand-Cartagena, Estibalitz
Soria de Diego, Francisco Javier
Tradacete Pérez, Pedro
author Durand-Cartagena, Estibalitz
author_facet Durand-Cartagena, Estibalitz
Soria de Diego, Francisco Javier
Tradacete Pérez, Pedro
author_role author
author2 Soria de Diego, Francisco Javier
Tradacete Pérez, Pedro
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv Doubling measure
Infinite graph
Spectral graph theory
Matemáticas (Matemáticas)
12 Matemáticas
topic Doubling measure
Infinite graph
Spectral graph theory
Matemáticas (Matemáticas)
12 Matemáticas
description We study the least doubling constant among all possible doubling measures defined on a (finite or infinite) graph G. We show that this constant can be estimated from below by 1 + r(AG ), where r(AG ) is the spectral radius of the adjacency matrix of G, and study when both quantities coincide. We also illustrate how amenability of the automorphism group of a graph can be related to finding doubling minimizers. Finally, we give a complete characterization of graphs with doubling constant smaller than 3, in the spirit of Smith graphs.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-01-01
2023
2023-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/105183
url https://hdl.handle.net/20.500.14352/105183
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PGC2018-097286-B-I00 ANALISIS FUNCIONAL NO LINEAL Y GEOMETRICO
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113048GB-I00 ESPACIOS DE FUNCIONES Y TECNICAS DE ACOTACION DE OPERADORES EN ANALISIS
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-116398GB-I00 APLICACIONES DEL ANALISIS FUNCIONAL EN PROBLEMAS DE GEOMETRIA Y TEORIA DE LA INFORMACION
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/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 4.0 International
http://creativecommons.org/licenses/by/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:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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