A note on the order of iterated line digraphs

Given a digraph G, we propose a new method to find the recurrence equation for the number of vertices n_k of the k-iterated line digraph L_k(G), for k>= 0, where L_0(G) = G. We obtain this result by using the minimal polynomial of a quotient digraph pi(G) of G. We show some examples of this metho...

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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:2016
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:2117/89923
Acceso en línea:https://hdl.handle.net/2117/89923
https://dx.doi.org/10.1002/jgt.22068
Access Level:acceso abierto
Palabra clave:Graph theory
Line digraph
adjacency matrix
minimal polynomial
regular partition
quotient digraph
recurrence
Teoria de grafs
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 A note on the order of iterated line digraphsDalfó Simó, Cristina|||0000-0002-8438-9353Fiol Mora, Miquel Àngel|||0000-0003-1337-4952Graph theoryLine digraphadjacency matrixminimal polynomialregular partitionquotient digraphrecurrenceTeoria de grafsClassificació AMS::05 Combinatorics::05C Graph theoryÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafsGiven a digraph G, we propose a new method to find the recurrence equation for the number of vertices n_k of the k-iterated line digraph L_k(G), for k>= 0, where L_0(G) = G. We obtain this result by using the minimal polynomial of a quotient digraph pi(G) of G. We show some examples of this method applied to the so-called cyclic Kautz, the unicyclic, and the acyclic digraphs. In the first case, our method gives the enumeration of the ternary length-2 squarefree words of any length.Peer ReviewedWiley20162016-07-2720162016-09-14journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/89923https://dx.doi.org/10.1002/jgt.22068reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengMinisterio de Economía y Competitividad http://doi.org/10.13039/501100003329 MTM2014-60127-P TECNICAS DE OPTIMIZACION EN TEORIA DE GRAFOS, GRUPOS Y COMBINATORIA. APLICACIONES A REDES, ALGORITMOS Y PROTOCOLOS DE COMUNICACION.open 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:2117/899232026-05-27T15:37:01Z
dc.title.none.fl_str_mv A note on the order of iterated line digraphs
title A note on the order of iterated line digraphs
spellingShingle A note on the order of iterated line digraphs
Dalfó Simó, Cristina|||0000-0002-8438-9353
Graph theory
Line digraph
adjacency matrix
minimal polynomial
regular partition
quotient digraph
recurrence
Teoria de grafs
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
title_short A note on the order of iterated line digraphs
title_full A note on the order of iterated line digraphs
title_fullStr A note on the order of iterated line digraphs
title_full_unstemmed A note on the order of iterated line digraphs
title_sort A note on the order of iterated line 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
Line digraph
adjacency matrix
minimal polynomial
regular partition
quotient digraph
recurrence
Teoria de grafs
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
topic Graph theory
Line digraph
adjacency matrix
minimal polynomial
regular partition
quotient digraph
recurrence
Teoria de grafs
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
description Given a digraph G, we propose a new method to find the recurrence equation for the number of vertices n_k of the k-iterated line digraph L_k(G), for k>= 0, where L_0(G) = G. We obtain this result by using the minimal polynomial of a quotient digraph pi(G) of G. We show some examples of this method applied to the so-called cyclic Kautz, the unicyclic, and the acyclic digraphs. In the first case, our method gives the enumeration of the ternary length-2 squarefree words of any length.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-07-27
2016
2016-09-14
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/89923
https://dx.doi.org/10.1002/jgt.22068
url https://hdl.handle.net/2117/89923
https://dx.doi.org/10.1002/jgt.22068
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://doi.org/10.13039/501100003329 MTM2014-60127-P TECNICAS DE OPTIMIZACION EN TEORIA DE GRAFOS, GRUPOS Y COMBINATORIA. APLICACIONES A REDES, ALGORITMOS Y PROTOCOLOS DE COMUNICACION.
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.publisher.none.fl_str_mv Wiley
publisher.none.fl_str_mv Wiley
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 15,301603

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