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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Authors: Dalfó, Cristina, Fiol Mora, Miguel Ángel
Format: article
Status:Published version
Publication Date:2021
Country:España
Institution:Universitat de Lleida (UdL)
Repository:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/72285
Online Access:https://doi.org/10.5614/ejgta.2021.9.2.22
http://hdl.handle.net/10459.1/72285
Access Level:Open access
Keyword:n-step Fibonacci number
Fibonacci graph
Digraph on alphabet
de Bruijn digraph
Line digraph
Adjacency matrix
Spectrum
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spelling On d-Fibonacci digraphsDalfó, CristinaFiol Mora, Miguel Ángeln-step Fibonacci numberFibonacci graphDigraph on alphabetde Bruijn digraphLine digraphAdjacency matrixSpectrumThe 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.The research of the first author has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 734922.Institut Teknologi Bandung (ITB) IndonesiaIndonesian Combinatorial Society (InaCombS)GTA Research Group, University of Newcastle (Australia)2021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://doi.org/10.5614/ejgta.2021.9.2.22http://hdl.handle.net/10459.1/72285https://creativecommons.org/licenses/by-sa/4.0/reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)InglésReproducció del document publicat a: https://doi.org/10.5614/ejgta.2021.9.2.22Electronic Journal of Graph Theory and Applications, 2021, vol. 9, num. 2, p. 527-538info:eu-repo/grantAgreement/EC/H2020/734922cc-by-sa (c) Dalfó et al., 2021info:eu-repo/semantics/openAccessoai:repositori.udl.cat:10459.1/722852026-06-24T12:42:17Z
dc.title.none.fl_str_mv On d-Fibonacci digraphs
title On d-Fibonacci digraphs
spellingShingle On d-Fibonacci digraphs
Dalfó, Cristina
n-step Fibonacci number
Fibonacci graph
Digraph on alphabet
de Bruijn digraph
Line digraph
Adjacency matrix
Spectrum
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, Cristina
Fiol Mora, Miguel Ángel
author Dalfó, Cristina
author_facet Dalfó, Cristina
Fiol Mora, Miguel Ángel
author_role author
author2 Fiol Mora, Miguel Ángel
author2_role author
dc.subject.none.fl_str_mv n-step Fibonacci number
Fibonacci graph
Digraph on alphabet
de Bruijn digraph
Line digraph
Adjacency matrix
Spectrum
topic n-step Fibonacci number
Fibonacci graph
Digraph on alphabet
de Bruijn digraph
Line digraph
Adjacency matrix
Spectrum
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
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/10.5614/ejgta.2021.9.2.22
http://hdl.handle.net/10459.1/72285
url https://doi.org/10.5614/ejgta.2021.9.2.22
http://hdl.handle.net/10459.1/72285
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/10.5614/ejgta.2021.9.2.22
Electronic Journal of Graph Theory and Applications, 2021, vol. 9, num. 2, p. 527-538
info:eu-repo/grantAgreement/EC/H2020/734922
dc.rights.none.fl_str_mv cc-by-sa (c) Dalfó et al., 2021
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-sa (c) Dalfó et al., 2021
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Institut Teknologi Bandung (ITB) Indonesia
Indonesian Combinatorial Society (InaCombS)
GTA Research Group, University of Newcastle (Australia)
publisher.none.fl_str_mv Institut Teknologi Bandung (ITB) Indonesia
Indonesian Combinatorial Society (InaCombS)
GTA Research Group, University of Newcastle (Australia)
dc.source.none.fl_str_mv https://creativecommons.org/licenses/by-sa/4.0/
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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score 15,81155

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