Small regular graphs of girth 7

In this paper, we construct new infinite families of regular graphs of girth 7 of smallest order known so far. Our constructions are based on combinatorial and geometric properties of (q + 1, 8)-cages, for q a prime power. We remove vertices from such cages and add matchings among the vertices of mi...

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Detalhes bibliográficos
Autores: Abreu, Marien, Araujo Pardo, Gabriela, Balbuena Martínez, Maria Camino Teófila|||0000-0003-4190-4287, Labbate, D., Salas Salvado, Jordi
Formato: artículo
Fecha de publicación:2015
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/86686
Acesso em linha:https://hdl.handle.net/2117/86686
Access Level:acceso abierto
Palavra-chave:Combinatorial analysis
Directed graphs
Cages
Girth
Incidence graph
Bipartite graphs
Construction
Anàlisi combinatòria
Grafs dirigits
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
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repository_id_str
spelling Small regular graphs of girth 7Abreu, MarienAraujo Pardo, GabrielaBalbuena Martínez, Maria Camino Teófila|||0000-0003-4190-4287Labbate, D.Salas Salvado, JordiCombinatorial analysisDirected graphsCagesGirthIncidence graphBipartite graphsConstructionCagesAnàlisi combinatòriaGrafs dirigitsÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::CombinatòriaIn this paper, we construct new infinite families of regular graphs of girth 7 of smallest order known so far. Our constructions are based on combinatorial and geometric properties of (q + 1, 8)-cages, for q a prime power. We remove vertices from such cages and add matchings among the vertices of minimum degree to achieve regularity in the new graphs. We obtain (q + 1)-regular graphs of girth 7 and order 2q(3) + q(2) + 2q for each even prime power q >= 4, and of order 2q(3) + 2q(2) q + 1 for each odd prime power q >= 5.20152015-07-0120162016-05-06journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/86686reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/866862026-05-27T15:37:01Z
dc.title.none.fl_str_mv Small regular graphs of girth 7
title Small regular graphs of girth 7
spellingShingle Small regular graphs of girth 7
Abreu, Marien
Combinatorial analysis
Directed graphs
Cages
Girth
Incidence graph
Bipartite graphs
Construction
Cages
Anàlisi combinatòria
Grafs dirigits
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
title_short Small regular graphs of girth 7
title_full Small regular graphs of girth 7
title_fullStr Small regular graphs of girth 7
title_full_unstemmed Small regular graphs of girth 7
title_sort Small regular graphs of girth 7
dc.creator.none.fl_str_mv Abreu, Marien
Araujo Pardo, Gabriela
Balbuena Martínez, Maria Camino Teófila|||0000-0003-4190-4287
Labbate, D.
Salas Salvado, Jordi
author Abreu, Marien
author_facet Abreu, Marien
Araujo Pardo, Gabriela
Balbuena Martínez, Maria Camino Teófila|||0000-0003-4190-4287
Labbate, D.
Salas Salvado, Jordi
author_role author
author2 Araujo Pardo, Gabriela
Balbuena Martínez, Maria Camino Teófila|||0000-0003-4190-4287
Labbate, D.
Salas Salvado, Jordi
author2_role author
author
author
author
dc.subject.none.fl_str_mv Combinatorial analysis
Directed graphs
Cages
Girth
Incidence graph
Bipartite graphs
Construction
Cages
Anàlisi combinatòria
Grafs dirigits
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
topic Combinatorial analysis
Directed graphs
Cages
Girth
Incidence graph
Bipartite graphs
Construction
Cages
Anàlisi combinatòria
Grafs dirigits
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
description In this paper, we construct new infinite families of regular graphs of girth 7 of smallest order known so far. Our constructions are based on combinatorial and geometric properties of (q + 1, 8)-cages, for q a prime power. We remove vertices from such cages and add matchings among the vertices of minimum degree to achieve regularity in the new graphs. We obtain (q + 1)-regular graphs of girth 7 and order 2q(3) + q(2) + 2q for each even prime power q >= 4, and of order 2q(3) + 2q(2) q + 1 for each odd prime power q >= 5.
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-07-01
2016
2016-05-06
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/2117/86686
url https://hdl.handle.net/2117/86686
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

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
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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score 15,300719

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