Moore mixed graphs from Cayley graphs

A Moore (r, z, k)-mixed graph G has every vertex with undirected degree r, directed in- and outdegree z, diameter k, and number of vertices (or order) attaining the corresponding Moore bound M(r, z, k) for mixed graphs. When the order of G is close to M(r, z, k) vertices, we refer to it as an almost...

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Detalhes bibliográficos
Autores: Dalfó Simó, Cristina|||0000-0002-8438-9353, Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
Formato: artículo
Fecha de publicación:2023
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:2117/387468
Acesso em linha:https://hdl.handle.net/2117/387468
https://dx.doi.org/10.5614/ejgta.2023.11.1.15
Access Level:acceso abierto
Palavra-chave:Graph theory
Group theory
Mixed graph
Moore bound
Cayley graph
Line digraph
Spectrum
Grafs, Teoria de
Grups, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Classificació AMS::20 Group theory and generalizations::20C Representation theory of groups
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups
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oai_identifier_str oai:upcommons.upc.edu:2117/387468
network_acronym_str ES
network_name_str España
repository_id_str
spelling Moore mixed graphs from Cayley graphsDalfó Simó, Cristina|||0000-0002-8438-9353Fiol Mora, Miquel Àngel|||0000-0003-1337-4952Graph theoryGroup theoryMixed graphMoore boundCayley graphLine digraphSpectrumGrafs, Teoria deGrups, Teoria deClassificació AMS::05 Combinatorics::05C Graph theoryClassificació AMS::20 Group theory and generalizations::20C Representation theory of groupsÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafsÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grupsA Moore (r, z, k)-mixed graph G has every vertex with undirected degree r, directed in- and outdegree z, diameter k, and number of vertices (or order) attaining the corresponding Moore bound M(r, z, k) for mixed graphs. When the order of G is close to M(r, z, k) vertices, we refer to it as an almost Moore graph. The first part of this paper is a survey about known Moore (and almost Moore) general mixed graphs that turn out to be Cayley graphs. Then, in the second part of the paper, we give new results on the bipartite case. First, we show that Moore bipartite mixed graphs with diameter three are distance-regular, and their spectra are fully characterized. In particular, an infinity family of Moore bipartite (1, z, 3)-mixed graphs is presented, which are Cayley graphs of semidirect products of groups. Our study is based on the line digraph technique, and on some results about when the line digraph of a Cayley digraph is again a Cayley digraph.This research has been partially supported by AGAUR from the Catalan Government under project 2021SGR00434 and MICINN from the Spanish Government under project PID2020-115442RBI00.Peer Reviewed20232023-03-2520232023-05-16journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/387468https://dx.doi.org/10.5614/ejgta.2023.11.1.15reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3874682026-05-27T15:37:01Z
dc.title.none.fl_str_mv Moore mixed graphs from Cayley graphs
title Moore mixed graphs from Cayley graphs
spellingShingle Moore mixed graphs from Cayley graphs
Dalfó Simó, Cristina|||0000-0002-8438-9353
Graph theory
Group theory
Mixed graph
Moore bound
Cayley graph
Line digraph
Spectrum
Grafs, Teoria de
Grups, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Classificació AMS::20 Group theory and generalizations::20C Representation theory of groups
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups
title_short Moore mixed graphs from Cayley graphs
title_full Moore mixed graphs from Cayley graphs
title_fullStr Moore mixed graphs from Cayley graphs
title_full_unstemmed Moore mixed graphs from Cayley graphs
title_sort Moore mixed graphs from Cayley graphs
dc.creator.none.fl_str_mv Dalfó Simó, Cristina|||0000-0002-8438-9353
Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
author Dalfó Simó, Cristina|||0000-0002-8438-9353
author_facet Dalfó Simó, Cristina|||0000-0002-8438-9353
Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
author_role author
author2 Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
author2_role author
dc.subject.none.fl_str_mv Graph theory
Group theory
Mixed graph
Moore bound
Cayley graph
Line digraph
Spectrum
Grafs, Teoria de
Grups, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Classificació AMS::20 Group theory and generalizations::20C Representation theory of groups
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups
topic Graph theory
Group theory
Mixed graph
Moore bound
Cayley graph
Line digraph
Spectrum
Grafs, Teoria de
Grups, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Classificació AMS::20 Group theory and generalizations::20C Representation theory of groups
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups
description A Moore (r, z, k)-mixed graph G has every vertex with undirected degree r, directed in- and outdegree z, diameter k, and number of vertices (or order) attaining the corresponding Moore bound M(r, z, k) for mixed graphs. When the order of G is close to M(r, z, k) vertices, we refer to it as an almost Moore graph. The first part of this paper is a survey about known Moore (and almost Moore) general mixed graphs that turn out to be Cayley graphs. Then, in the second part of the paper, we give new results on the bipartite case. First, we show that Moore bipartite mixed graphs with diameter three are distance-regular, and their spectra are fully characterized. In particular, an infinity family of Moore bipartite (1, z, 3)-mixed graphs is presented, which are Cayley graphs of semidirect products of groups. Our study is based on the line digraph technique, and on some results about when the line digraph of a Cayley digraph is again a Cayley digraph.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-03-25
2023
2023-05-16
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/2117/387468
https://dx.doi.org/10.5614/ejgta.2023.11.1.15
url https://hdl.handle.net/2117/387468
https://dx.doi.org/10.5614/ejgta.2023.11.1.15
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
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
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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