On Bipartite Biregular Large Graphs Derived From Difference Sets

A bipartite graph G = ( V , E ) with V = V 1 boolean OR V 2 is biregular if all the vertices of each stable set, V 1 and V 2 , have the same degree, r and s, respectively. This paper studies difference sets derived from both Abelian and non-Abelian groups. From them, we propose some constructions of...

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Detalhes bibliográficos
Autores: Araujo-Pardo, Gabriela, Dalfó, Cristina, Fiol Mora, Miguel Ángel, López Lorenzo, Ignacio
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Recursos:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/468068
Acesso em linha:https://doi.org/10.1002/jgt.23263
https://hdl.handle.net/10459.1/468068
Access Level:acceso abierto
Palavra-chave:Adjacency spectrum
Bipartite biregular graphs
Diameter
Moore bound
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spelling On Bipartite Biregular Large Graphs Derived From Difference SetsAraujo-Pardo, GabrielaDalfó, CristinaFiol Mora, Miguel ÁngelLópez Lorenzo, IgnacioAdjacency spectrumBipartite biregular graphsDiameterMoore boundA bipartite graph G = ( V , E ) with V = V 1 boolean OR V 2 is biregular if all the vertices of each stable set, V 1 and V 2 , have the same degree, r and s, respectively. This paper studies difference sets derived from both Abelian and non-Abelian groups. From them, we propose some constructions of bipartite biregular graphs with diameter d = 3 and asymptotically optimal order for given degrees r and s, meaning that asymptotically the order approaches a fixed multiple of the Moore bound. Moreover, we find some biMoore graphs, that is, bipartite biregular graphs that attain the Moore bound.The research of the Gabriela Araujo-Pardo is supported by PAPIIT-México under Project IN101821 and Proyecto de Intercambio Académico 1926: “Gráficas de Moore, Jaulas, Diseños de Bloques y Número Cromático”, CIC-UNAM. The research of Cristina Dalfó, Miquel Àngel Fiol, and Nacho López has been supported by AGAUR from the Catalan Government under project 2021SGR00434 and MICINN from the Spanish Government under project PID2020-115442RB-I00. The research of Miquel Àngel Fiol was also supported by a grant from the Universitat Politècnica de Catalunya with reference AGRUPS-2024.Wiley2025info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://doi.org/10.1002/jgt.23263https://hdl.handle.net/10459.1/468068reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)InglésReproducció del document publicat a https://doi.org/10.1002/jgt.23263Journal of Graph Therory, 2025, núm. art. 23263cc-by-nc-nd (c) Araujo-Pardo et al., 2025Attribution-NonCommercial-NoDerivatives 4.0 Internationalinfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/oai:repositori.udl.cat:10459.1/4680682026-06-24T12:42:17Z
dc.title.none.fl_str_mv On Bipartite Biregular Large Graphs Derived From Difference Sets
title On Bipartite Biregular Large Graphs Derived From Difference Sets
spellingShingle On Bipartite Biregular Large Graphs Derived From Difference Sets
Araujo-Pardo, Gabriela
Adjacency spectrum
Bipartite biregular graphs
Diameter
Moore bound
title_short On Bipartite Biregular Large Graphs Derived From Difference Sets
title_full On Bipartite Biregular Large Graphs Derived From Difference Sets
title_fullStr On Bipartite Biregular Large Graphs Derived From Difference Sets
title_full_unstemmed On Bipartite Biregular Large Graphs Derived From Difference Sets
title_sort On Bipartite Biregular Large Graphs Derived From Difference Sets
dc.creator.none.fl_str_mv Araujo-Pardo, Gabriela
Dalfó, Cristina
Fiol Mora, Miguel Ángel
López Lorenzo, Ignacio
author Araujo-Pardo, Gabriela
author_facet Araujo-Pardo, Gabriela
Dalfó, Cristina
Fiol Mora, Miguel Ángel
López Lorenzo, Ignacio
author_role author
author2 Dalfó, Cristina
Fiol Mora, Miguel Ángel
López Lorenzo, Ignacio
author2_role author
author
author
dc.subject.none.fl_str_mv Adjacency spectrum
Bipartite biregular graphs
Diameter
Moore bound
topic Adjacency spectrum
Bipartite biregular graphs
Diameter
Moore bound
description A bipartite graph G = ( V , E ) with V = V 1 boolean OR V 2 is biregular if all the vertices of each stable set, V 1 and V 2 , have the same degree, r and s, respectively. This paper studies difference sets derived from both Abelian and non-Abelian groups. From them, we propose some constructions of bipartite biregular graphs with diameter d = 3 and asymptotically optimal order for given degrees r and s, meaning that asymptotically the order approaches a fixed multiple of the Moore bound. Moreover, we find some biMoore graphs, that is, bipartite biregular graphs that attain the Moore bound.
publishDate 2025
dc.date.none.fl_str_mv 2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://doi.org/10.1002/jgt.23263
https://hdl.handle.net/10459.1/468068
url https://doi.org/10.1002/jgt.23263
https://hdl.handle.net/10459.1/468068
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a https://doi.org/10.1002/jgt.23263
Journal of Graph Therory, 2025, núm. art. 23263
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Araujo-Pardo et al., 2025
Attribution-NonCommercial-NoDerivatives 4.0 International
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/
rights_invalid_str_mv cc-by-nc-nd (c) Araujo-Pardo et al., 2025
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Wiley
publisher.none.fl_str_mv Wiley
dc.source.none.fl_str_mv reponame:Repositori Obert UdL
instname:Universitat de Lleida (UdL)
instname_str Universitat de Lleida (UdL)
reponame_str Repositori Obert UdL
collection Repositori Obert UdL
repository.name.fl_str_mv
repository.mail.fl_str_mv
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