On New Record Graphs Close to Bipartite Moore Graphs

The modelling of interconnection networks by graphs motivated the study of several extremal problems that involve well known parameters of a graph (degree, diameter, girth and order) and optimising one of the parameters given restrictions on some of the others. Here we focus on bipartite Moore graph...

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Detalhes bibliográficos
Autores: Araujo Pardo, Martha Gabriela, López Lorenzo, Ignacio
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2022
País:España
Recursos:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/84463
Acesso em linha:https://doi.org/10.1007/s00373-022-02500-3
http://hdl.handle.net/10459.1/84463
Access Level:acceso abierto
Palavra-chave:Bipartite Moore bound
Bipartite graph
Girth
Local girth
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spelling On New Record Graphs Close to Bipartite Moore GraphsAraujo Pardo, Martha GabrielaLópez Lorenzo, IgnacioBipartite Moore boundBipartite graphGirthLocal girthThe modelling of interconnection networks by graphs motivated the study of several extremal problems that involve well known parameters of a graph (degree, diameter, girth and order) and optimising one of the parameters given restrictions on some of the others. Here we focus on bipartite Moore graphs, that is, bipartite graphs attaining the optimum order, fixed either the degree/diameter or degree/girth. The fact that there are very few bipartite Moore graphs suggests the relaxation of some of the constraints implied by the bipartite Moore bound. First we deal with local bipartite Moore graphs. We find in some cases those local bipartite Moore graphs with local girths as close as possible to the local girths given by a bipartite Moore graph. Second, we construct a family of (q+2)-bipartite graphs of order 2(q2+q+5) and diameter 3, for q a power of prime. These graphs attain the record value for q=9 and improve the values for q=11 and q=13.Research of N. López was supported in part by the MCIN/AEI/10.13039/501100011033 through Grant PID2020-115442RB-I00 (Spanish Ministerio de Ciencia e Innovacion) and research of G. Araujo was supported by PASPA-DGAPA and CONACyT Sabbatical Stay 2020, CONACyT-México under Project 282280, 47510664 and PAPIIT-México under Projects IN107218, IN108121.Springer Nature2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionhttps://doi.org/10.1007/s00373-022-02500-3http://hdl.handle.net/10459.1/84463reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)Inglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-115442RB-I00Versió postprint del document publicat a https://doi.org/10.1007/s00373-022-02500-3Graphs and Combinatorics, 2022, vol. 38, art. 110.(c) Springer Nature, 2022info:eu-repo/semantics/openAccessoai:repositori.udl.cat:10459.1/844632026-06-24T12:42:17Z
dc.title.none.fl_str_mv On New Record Graphs Close to Bipartite Moore Graphs
title On New Record Graphs Close to Bipartite Moore Graphs
spellingShingle On New Record Graphs Close to Bipartite Moore Graphs
Araujo Pardo, Martha Gabriela
Bipartite Moore bound
Bipartite graph
Girth
Local girth
title_short On New Record Graphs Close to Bipartite Moore Graphs
title_full On New Record Graphs Close to Bipartite Moore Graphs
title_fullStr On New Record Graphs Close to Bipartite Moore Graphs
title_full_unstemmed On New Record Graphs Close to Bipartite Moore Graphs
title_sort On New Record Graphs Close to Bipartite Moore Graphs
dc.creator.none.fl_str_mv Araujo Pardo, Martha Gabriela
López Lorenzo, Ignacio
author Araujo Pardo, Martha Gabriela
author_facet Araujo Pardo, Martha Gabriela
López Lorenzo, Ignacio
author_role author
author2 López Lorenzo, Ignacio
author2_role author
dc.subject.none.fl_str_mv Bipartite Moore bound
Bipartite graph
Girth
Local girth
topic Bipartite Moore bound
Bipartite graph
Girth
Local girth
description The modelling of interconnection networks by graphs motivated the study of several extremal problems that involve well known parameters of a graph (degree, diameter, girth and order) and optimising one of the parameters given restrictions on some of the others. Here we focus on bipartite Moore graphs, that is, bipartite graphs attaining the optimum order, fixed either the degree/diameter or degree/girth. The fact that there are very few bipartite Moore graphs suggests the relaxation of some of the constraints implied by the bipartite Moore bound. First we deal with local bipartite Moore graphs. We find in some cases those local bipartite Moore graphs with local girths as close as possible to the local girths given by a bipartite Moore graph. Second, we construct a family of (q+2)-bipartite graphs of order 2(q2+q+5) and diameter 3, for q a power of prime. These graphs attain the record value for q=9 and improve the values for q=11 and q=13.
publishDate 2022
dc.date.none.fl_str_mv 2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://doi.org/10.1007/s00373-022-02500-3
http://hdl.handle.net/10459.1/84463
url https://doi.org/10.1007/s00373-022-02500-3
http://hdl.handle.net/10459.1/84463
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-115442RB-I00
Versió postprint del document publicat a https://doi.org/10.1007/s00373-022-02500-3
Graphs and Combinatorics, 2022, vol. 38, art. 110.
dc.rights.none.fl_str_mv (c) Springer Nature, 2022
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Springer Nature, 2022
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer Nature
publisher.none.fl_str_mv Springer Nature
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
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repository.mail.fl_str_mv
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