The Manhattan Product of Digraphs

We study the main properties of a new product of bipartite digraphs which we call Manhattan product. This product allows us to understand the subjacent product in the Manhattan street networks and can be used to built other networks with similar good properties. It is shown that if all the factors o...

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Detalles Bibliográficos
Autores: Comellas Padró, Francesc, Dalfó, Cristina, Fiol Mora, Miguel Ángel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2013
País:España
Institución:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/65706
Acceso en línea:https://doi.org/10.5614/ejgta.2013.1.1.2
http://hdl.handle.net/10459.1/65706
Access Level:acceso abierto
Palabra clave:Self-converse digraph
Manhattan street network
Unilateral diameter
Cayley digraph
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spelling The Manhattan Product of DigraphsComellas Padró, FrancescDalfó, CristinaFiol Mora, Miguel ÁngelSelf-converse digraphManhattan street networkUnilateral diameterCayley digraphWe study the main properties of a new product of bipartite digraphs which we call Manhattan product. This product allows us to understand the subjacent product in the Manhattan street networks and can be used to built other networks with similar good properties. It is shown that if all the factors of such a product are (directed) cycles, then the digraph obtained is a Manhattan street network, a widely studied topology for modeling some interconnection networks. To this respect, it is proved that many properties of these networks, such as high symmetries, reduced diameter and the presence of Hamiltonian cycles, are shared by the Manhattan product of some digraphs. Moreover, we show that the Manhattan product of two Manhattan streets networks is also a Manhattan street network. Finally, some sufficient conditions for the Manhattan product of two Cayley digraphs to be also a Cayley digraph are given. Throughout our study we use some interesting recent concepts, such as the unilateral distance and related graph invariants.This research was supported by the Ministry of Science and Innovation (Spain) and the European Regional Development Fund under project MTM2011-28800-C02-01-1 and by the Catalan Research Council under project 2009SGR1387.Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia2013info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://doi.org/10.5614/ejgta.2013.1.1.2http://hdl.handle.net/10459.1/65706reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)Inglésinfo:eu-repo/grantAgreement/MICINN//MTM2011-28800-C02-01Reproducció del document publicat a https://doi.org/10.5614/ejgta.2013.1.1.2Electronic Journal of Graph Theory and Applications, 2013, vol. 1, núm. 1, p. 11–27cc-by-sa (c) F. Comellas et al., 2013info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-sa/4.0/oai:repositori.udl.cat:10459.1/657062026-06-24T12:42:17Z
dc.title.none.fl_str_mv The Manhattan Product of Digraphs
title The Manhattan Product of Digraphs
spellingShingle The Manhattan Product of Digraphs
Comellas Padró, Francesc
Self-converse digraph
Manhattan street network
Unilateral diameter
Cayley digraph
title_short The Manhattan Product of Digraphs
title_full The Manhattan Product of Digraphs
title_fullStr The Manhattan Product of Digraphs
title_full_unstemmed The Manhattan Product of Digraphs
title_sort The Manhattan Product of Digraphs
dc.creator.none.fl_str_mv Comellas Padró, Francesc
Dalfó, Cristina
Fiol Mora, Miguel Ángel
author Comellas Padró, Francesc
author_facet Comellas Padró, Francesc
Dalfó, Cristina
Fiol Mora, Miguel Ángel
author_role author
author2 Dalfó, Cristina
Fiol Mora, Miguel Ángel
author2_role author
author
dc.subject.none.fl_str_mv Self-converse digraph
Manhattan street network
Unilateral diameter
Cayley digraph
topic Self-converse digraph
Manhattan street network
Unilateral diameter
Cayley digraph
description We study the main properties of a new product of bipartite digraphs which we call Manhattan product. This product allows us to understand the subjacent product in the Manhattan street networks and can be used to built other networks with similar good properties. It is shown that if all the factors of such a product are (directed) cycles, then the digraph obtained is a Manhattan street network, a widely studied topology for modeling some interconnection networks. To this respect, it is proved that many properties of these networks, such as high symmetries, reduced diameter and the presence of Hamiltonian cycles, are shared by the Manhattan product of some digraphs. Moreover, we show that the Manhattan product of two Manhattan streets networks is also a Manhattan street network. Finally, some sufficient conditions for the Manhattan product of two Cayley digraphs to be also a Cayley digraph are given. Throughout our study we use some interesting recent concepts, such as the unilateral distance and related graph invariants.
publishDate 2013
dc.date.none.fl_str_mv 2013
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.2013.1.1.2
http://hdl.handle.net/10459.1/65706
url https://doi.org/10.5614/ejgta.2013.1.1.2
http://hdl.handle.net/10459.1/65706
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MICINN//MTM2011-28800-C02-01
Reproducció del document publicat a https://doi.org/10.5614/ejgta.2013.1.1.2
Electronic Journal of Graph Theory and Applications, 2013, vol. 1, núm. 1, p. 11–27
dc.rights.none.fl_str_mv cc-by-sa (c) F. Comellas et al., 2013
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-sa/4.0/
rights_invalid_str_mv cc-by-sa (c) F. Comellas et al., 2013
http://creativecommons.org/licenses/by-sa/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia
publisher.none.fl_str_mv Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia
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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score 15,812429

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