The diameter of cyclic Kautz digraphs

We present a new kind of digraphs, called cyclic Kautz digraphs CK(d, ɭ), which are subdigraphs of the well-known Kautz digraphs K(d,ɭ). The latter have the smallest diameter among all digraphs with their number of vertices and degree. Cyclic Kautz digraphs CK(d, ɭ) have vertices labeled by all poss...

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Detalles Bibliográficos
Autores: Böhmová, Katerina, Dalfó, Cristina, Huemer, Clemens
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2017
País:España
Institución:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/66757
Acceso en línea:https://doi.org/10.2298/FIL1720551B
http://hdl.handle.net/10459.1/66757
Access Level:acceso abierto
Palabra clave:Digraph
Diameter
Kautz digraph
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spelling The diameter of cyclic Kautz digraphsBöhmová, KaterinaDalfó, CristinaHuemer, ClemensDigraphDiameterKautz digraphWe present a new kind of digraphs, called cyclic Kautz digraphs CK(d, ɭ), which are subdigraphs of the well-known Kautz digraphs K(d,ɭ). The latter have the smallest diameter among all digraphs with their number of vertices and degree. Cyclic Kautz digraphs CK(d, ɭ) have vertices labeled by all possible sequences a1 . . . aɭ of length ɭ, such that each character ai is chosen from an alphabet containing d + 1 distinct symbols, where the consecutive characters in the sequence are different (as in Kautz digraphs), and now also requiring that a1 ≠ aɭ. Their arcs are between vertices a1a2 . . . aɭ and a2 . . . aɭ aɭ + 1, with a1 ≠ aɭ and a2 ≠ aɭ + 1. We give the diameter of CK(d, ɭ) for all the values of d and ɭ, and also its number of vertices and arcs.Research of C. Dalfo is supported by projects MINECO MTM2014-60127-P, and AGAUR 2014SGR1147. Research of C. Huemer is supported by projects MINECO MTM2015-63791-R, and AGAUR 2014SGR46. C. Dalfo and C. Huemer have also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie SkłodowskaCurie grant agreement No 734922.Faculty of Sciences and Mathematics, University of Nis, Serbia2017info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://doi.org/10.2298/FIL1720551Bhttp://hdl.handle.net/10459.1/66757reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)Inglésinfo:eu-repo/grantAgreement/MINECO//MTM2014-60127-PVersió postprint del document publicat a: https://doi.org/10.2298/FIL1720551BFilomat, 2017, vol. 31, núm. 20, p. 6551-6560info:eu-repo/grantAgreement/EC/H2020/734922cc-by-nc-nd (c) Böhmová, Katerina et al., 2017info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.caoai:repositori.udl.cat:10459.1/667572026-06-24T12:42:17Z
dc.title.none.fl_str_mv The diameter of cyclic Kautz digraphs
title The diameter of cyclic Kautz digraphs
spellingShingle The diameter of cyclic Kautz digraphs
Böhmová, Katerina
Digraph
Diameter
Kautz digraph
title_short The diameter of cyclic Kautz digraphs
title_full The diameter of cyclic Kautz digraphs
title_fullStr The diameter of cyclic Kautz digraphs
title_full_unstemmed The diameter of cyclic Kautz digraphs
title_sort The diameter of cyclic Kautz digraphs
dc.creator.none.fl_str_mv Böhmová, Katerina
Dalfó, Cristina
Huemer, Clemens
author Böhmová, Katerina
author_facet Böhmová, Katerina
Dalfó, Cristina
Huemer, Clemens
author_role author
author2 Dalfó, Cristina
Huemer, Clemens
author2_role author
author
dc.subject.none.fl_str_mv Digraph
Diameter
Kautz digraph
topic Digraph
Diameter
Kautz digraph
description We present a new kind of digraphs, called cyclic Kautz digraphs CK(d, ɭ), which are subdigraphs of the well-known Kautz digraphs K(d,ɭ). The latter have the smallest diameter among all digraphs with their number of vertices and degree. Cyclic Kautz digraphs CK(d, ɭ) have vertices labeled by all possible sequences a1 . . . aɭ of length ɭ, such that each character ai is chosen from an alphabet containing d + 1 distinct symbols, where the consecutive characters in the sequence are different (as in Kautz digraphs), and now also requiring that a1 ≠ aɭ. Their arcs are between vertices a1a2 . . . aɭ and a2 . . . aɭ aɭ + 1, with a1 ≠ aɭ and a2 ≠ aɭ + 1. We give the diameter of CK(d, ɭ) for all the values of d and ɭ, and also its number of vertices and arcs.
publishDate 2017
dc.date.none.fl_str_mv 2017
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://doi.org/10.2298/FIL1720551B
http://hdl.handle.net/10459.1/66757
url https://doi.org/10.2298/FIL1720551B
http://hdl.handle.net/10459.1/66757
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MINECO//MTM2014-60127-P
Versió postprint del document publicat a: https://doi.org/10.2298/FIL1720551B
Filomat, 2017, vol. 31, núm. 20, p. 6551-6560
info:eu-repo/grantAgreement/EC/H2020/734922
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Böhmová, Katerina et al., 2017
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/deed.ca
rights_invalid_str_mv cc-by-nc-nd (c) Böhmová, Katerina et al., 2017
http://creativecommons.org/licenses/by-nc-nd/4.0/deed.ca
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Faculty of Sciences and Mathematics, University of Nis, Serbia
publisher.none.fl_str_mv Faculty of Sciences and Mathematics, University of Nis, Serbia
dc.source.none.fl_str_mv 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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