From subkautz digraphs to cyclic kautz digraphs

Kautz digraphs K(d,l) are a well-known family of dense digraphs, widely studied as a good model for interconnection networks. Closely related with these, the cyclic Kautz digraphs CK(d,l) were recently introduced by Böhmová, Huemer and the author, and some of its distance-related parameters were fix...

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Detalles Bibliográficos
Autor: Dalfó Simó, Cristina|||0000-0002-8438-9353
Tipo de recurso: artículo
Fecha de publicación:2018
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:2117/125611
Acceso en línea:https://hdl.handle.net/2117/125611
https://dx.doi.org/10.1142/S0219265918500068
Access Level:acceso abierto
Palabra clave:Matrices
Directed graphs
Digraph
Distance
Diameter
Mean distance
Routing
Kautz digraph
Line digraph
(Vertex-)connectivity
Edge-connectivity
Superconnectivity
semigirth
Girth
Matrius (Matemàtica)
Grafs dirigits
Àrees temàtiques de la UPC::Matemàtiques i estadística
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oai_identifier_str oai:upcommons.upc.edu:2117/125611
network_acronym_str ES
network_name_str España
repository_id_str
spelling From subkautz digraphs to cyclic kautz digraphsDalfó Simó, Cristina|||0000-0002-8438-9353MatricesDirected graphsDigraphDistanceDiameterMean distanceRoutingKautz digraphLine digraph(Vertex-)connectivityEdge-connectivitySuperconnectivitysemigirthGirthMatrius (Matemàtica)Grafs dirigitsÀrees temàtiques de la UPC::Matemàtiques i estadísticaKautz digraphs K(d,l) are a well-known family of dense digraphs, widely studied as a good model for interconnection networks. Closely related with these, the cyclic Kautz digraphs CK(d,l) were recently introduced by Böhmová, Huemer and the author, and some of its distance-related parameters were fixed. In this paper we propose a new approach to cyclic Kautz digraphs by introducing the family of subKautz digraphs sK(d,l), from where the cyclic Kautz digraphs can be obtained as line digraphs. This allows us to give exact formulas for the distance between any two vertices of both sK(d,l) and CK(d,l). Moreover, we compute the diameter and the semigirth of both families, also providing efficient routing algorithms to find the shortest path between any pair of vertices. Using these parameters, we also prove that sK(d,l) and CK(d,l) are maximally vertex-connected and super-edge-connected. Whereas K(d,l) are optimal with respect to the diameter, we show that sK(d,l) and CK(d,l) are optimal with respect to the mean distance, whose exact values are given for both families when l = 3. Finally, we provide a lower bound on the girth of CK(d,l) and sK(d,l)Peer Reviewed20182018-06-0120182018-12-11journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/125611https://dx.doi.org/10.1142/S0219265918500068reponame: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_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1256112026-05-27T15:37:01Z
dc.title.none.fl_str_mv From subkautz digraphs to cyclic kautz digraphs
title From subkautz digraphs to cyclic kautz digraphs
spellingShingle From subkautz digraphs to cyclic kautz digraphs
Dalfó Simó, Cristina|||0000-0002-8438-9353
Matrices
Directed graphs
Digraph
Distance
Diameter
Mean distance
Routing
Kautz digraph
Line digraph
(Vertex-)connectivity
Edge-connectivity
Superconnectivity
semigirth
Girth
Matrius (Matemàtica)
Grafs dirigits
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short From subkautz digraphs to cyclic kautz digraphs
title_full From subkautz digraphs to cyclic kautz digraphs
title_fullStr From subkautz digraphs to cyclic kautz digraphs
title_full_unstemmed From subkautz digraphs to cyclic kautz digraphs
title_sort From subkautz digraphs to cyclic kautz digraphs
dc.creator.none.fl_str_mv Dalfó Simó, Cristina|||0000-0002-8438-9353
author Dalfó Simó, Cristina|||0000-0002-8438-9353
author_facet Dalfó Simó, Cristina|||0000-0002-8438-9353
author_role author
dc.subject.none.fl_str_mv Matrices
Directed graphs
Digraph
Distance
Diameter
Mean distance
Routing
Kautz digraph
Line digraph
(Vertex-)connectivity
Edge-connectivity
Superconnectivity
semigirth
Girth
Matrius (Matemàtica)
Grafs dirigits
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Matrices
Directed graphs
Digraph
Distance
Diameter
Mean distance
Routing
Kautz digraph
Line digraph
(Vertex-)connectivity
Edge-connectivity
Superconnectivity
semigirth
Girth
Matrius (Matemàtica)
Grafs dirigits
Àrees temàtiques de la UPC::Matemàtiques i estadística
description Kautz digraphs K(d,l) are a well-known family of dense digraphs, widely studied as a good model for interconnection networks. Closely related with these, the cyclic Kautz digraphs CK(d,l) were recently introduced by Böhmová, Huemer and the author, and some of its distance-related parameters were fixed. In this paper we propose a new approach to cyclic Kautz digraphs by introducing the family of subKautz digraphs sK(d,l), from where the cyclic Kautz digraphs can be obtained as line digraphs. This allows us to give exact formulas for the distance between any two vertices of both sK(d,l) and CK(d,l). Moreover, we compute the diameter and the semigirth of both families, also providing efficient routing algorithms to find the shortest path between any pair of vertices. Using these parameters, we also prove that sK(d,l) and CK(d,l) are maximally vertex-connected and super-edge-connected. Whereas K(d,l) are optimal with respect to the diameter, we show that sK(d,l) and CK(d,l) are optimal with respect to the mean distance, whose exact values are given for both families when l = 3. Finally, we provide a lower bound on the girth of CK(d,l) and sK(d,l)
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-06-01
2018
2018-12-11
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/2117/125611
https://dx.doi.org/10.1142/S0219265918500068
url https://hdl.handle.net/2117/125611
https://dx.doi.org/10.1142/S0219265918500068
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
Attribution-NonCommercial-NoDerivs 3.0 Spain
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
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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 15.300724

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