On d-Fibonacci digraphs

The d-Fibonacci digraphs F(d, k), introduced here, have the number of vertices following some generalized Fibonacci-like sequences. They can be defined both as digraphs on alphabets and as iterated line digraphs. Here we study some of their nice properties. For instance, F(d, k) has diameter d + k -...

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Detalles Bibliográficos
Autores: Dalfó Simó, Cristina|||0000-0002-8438-9353, Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/357037
Acceso en línea:https://hdl.handle.net/2117/357037
https://dx.doi.org/10.5614/ejgta.2021.9.2.22
Access Level:acceso abierto
Palabra clave:Graph theory
N-step Fibonacci number
Fibonacci graph
Digraph on alphabet
De Bruijn digraph
Line digraph
Adjacency matrix
Spectrum
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
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spelling On d-Fibonacci digraphsDalfó Simó, Cristina|||0000-0002-8438-9353Fiol Mora, Miquel Àngel|||0000-0003-1337-4952Graph theoryN-step Fibonacci numberFibonacci graphDigraph on alphabetDe Bruijn digraphLine digraphAdjacency matrixSpectrumGrafs, Teoria deClassificació AMS::05 Combinatorics::05C Graph theoryÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafsThe d-Fibonacci digraphs F(d, k), introduced here, have the number of vertices following some generalized Fibonacci-like sequences. They can be defined both as digraphs on alphabets and as iterated line digraphs. Here we study some of their nice properties. For instance, F(d, k) has diameter d + k - 2 and is semi-pancyclic; that is, it has a cycle of every length between 1 and l, with l ¿ {2k - 2, 2k - 1}. Moreover, it turns out that several other numbers of F(d, k) (of closed l-walks, classes of vertices, etc.) also follow the same linear recurrences as the numbers of vertices of the d-Fibonacci digraphs.This research has been partially supported by AGAUR from the Catalan Government under project 2017SGR1087 and by MICINN from the Spanish Government under project PGC2018-095471-B-I00. The research of the first author has also been supported by MICINN from the Spanish Government under project MTM2017-83271-R. The research of the first author has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 734922.Peer Reviewed20212021-10-0320212021-11-24journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/357037https://dx.doi.org/10.5614/ejgta.2021.9.2.22reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengEuropean Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 734922 Combinatorics of Networks and Computationopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3570372026-05-27T15:37:01Z
dc.title.none.fl_str_mv On d-Fibonacci digraphs
title On d-Fibonacci digraphs
spellingShingle On d-Fibonacci digraphs
Dalfó Simó, Cristina|||0000-0002-8438-9353
Graph theory
N-step Fibonacci number
Fibonacci graph
Digraph on alphabet
De Bruijn digraph
Line digraph
Adjacency matrix
Spectrum
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
title_short On d-Fibonacci digraphs
title_full On d-Fibonacci digraphs
title_fullStr On d-Fibonacci digraphs
title_full_unstemmed On d-Fibonacci digraphs
title_sort On d-Fibonacci digraphs
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
N-step Fibonacci number
Fibonacci graph
Digraph on alphabet
De Bruijn digraph
Line digraph
Adjacency matrix
Spectrum
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
topic Graph theory
N-step Fibonacci number
Fibonacci graph
Digraph on alphabet
De Bruijn digraph
Line digraph
Adjacency matrix
Spectrum
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
description The d-Fibonacci digraphs F(d, k), introduced here, have the number of vertices following some generalized Fibonacci-like sequences. They can be defined both as digraphs on alphabets and as iterated line digraphs. Here we study some of their nice properties. For instance, F(d, k) has diameter d + k - 2 and is semi-pancyclic; that is, it has a cycle of every length between 1 and l, with l ¿ {2k - 2, 2k - 1}. Moreover, it turns out that several other numbers of F(d, k) (of closed l-walks, classes of vertices, etc.) also follow the same linear recurrences as the numbers of vertices of the d-Fibonacci digraphs.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-10-03
2021
2021-11-24
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/2117/357037
https://dx.doi.org/10.5614/ejgta.2021.9.2.22
url https://hdl.handle.net/2117/357037
https://dx.doi.org/10.5614/ejgta.2021.9.2.22
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 734922 Combinatorics of Networks and Computation
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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