The hierarchical product of graphs

A new operation on graphs is introduced and some of its properties are studied. We call it hierarchical product, because of the strong (connectedness) hierarchy of the vertices in the resulting graphs. In fact, the obtained graphs turn out to be subgraphs of the cartesian product of the correspondin...

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Detalles Bibliográficos
Autores: Barrière, Lali, Comellas Padró, Francesc, Dalfó, Cristina, Fiol Mora, Miguel Ángel
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2009
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10459.1/463314
Acceso en línea:https://doi.org/10.1016/j.dam.2008.04.018
https://hdl.handle.net/10459.1/463314
Access Level:acceso abierto
Palabra clave:Graph operations
Hierarchical product
Diameter
Mean distance
Adjacency matrix
Eigenvalues
Characteristic polynomial
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spelling The hierarchical product of graphsBarrière, LaliComellas Padró, FrancescDalfó, CristinaFiol Mora, Miguel ÁngelGraph operationsHierarchical productDiameterMean distanceAdjacency matrixEigenvaluesCharacteristic polynomialA new operation on graphs is introduced and some of its properties are studied. We call it hierarchical product, because of the strong (connectedness) hierarchy of the vertices in the resulting graphs. In fact, the obtained graphs turn out to be subgraphs of the cartesian product of the corresponding factors. Some well-known properties of the cartesian product, such as reduced mean distance and diameter, simple routing algorithms and some optimal communication protocols are inherited by the hierarchical product. We also address the study of some algebraic properties of the hierarchical product of two or more graphs. In particular, the spectrum of the binary hypertree Tm (which is the hierarchical product of several copies of the complete graph on two vertices) is fully characterized; turning out to be an interesting example of graph with all its eigenvalues distinct. Finally, some natural generalizations of the hierarchic product are proposed.This research was supported by the Ministry of Education and Science (Spain) and the European Regional Development Fund (ERR) under projects MTM2005-08990-C02-01 and TEC2005-03575.Elsevier2009info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionhttps://doi.org/10.1016/j.dam.2008.04.018https://hdl.handle.net/10459.1/463314reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésVersió preprint del document publicat a: https://doi.org/10.1016/j.dam.2008.04.018Discrete Applied Mathematics, 2009, vol. 157, p. 36-48Discrete Applied Mathematicscc-by-nc-nd, (c) Elsevier, 2009Attribution-NonCommercial-NoDerivatives 4.0 Internationalinfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/oai:recercat.cat:10459.1/4633142026-05-29T05:05:01Z
dc.title.none.fl_str_mv The hierarchical product of graphs
title The hierarchical product of graphs
spellingShingle The hierarchical product of graphs
Barrière, Lali
Graph operations
Hierarchical product
Diameter
Mean distance
Adjacency matrix
Eigenvalues
Characteristic polynomial
title_short The hierarchical product of graphs
title_full The hierarchical product of graphs
title_fullStr The hierarchical product of graphs
title_full_unstemmed The hierarchical product of graphs
title_sort The hierarchical product of graphs
dc.creator.none.fl_str_mv Barrière, Lali
Comellas Padró, Francesc
Dalfó, Cristina
Fiol Mora, Miguel Ángel
author Barrière, Lali
author_facet Barrière, Lali
Comellas Padró, Francesc
Dalfó, Cristina
Fiol Mora, Miguel Ángel
author_role author
author2 Comellas Padró, Francesc
Dalfó, Cristina
Fiol Mora, Miguel Ángel
author2_role author
author
author
dc.subject.none.fl_str_mv Graph operations
Hierarchical product
Diameter
Mean distance
Adjacency matrix
Eigenvalues
Characteristic polynomial
topic Graph operations
Hierarchical product
Diameter
Mean distance
Adjacency matrix
Eigenvalues
Characteristic polynomial
description A new operation on graphs is introduced and some of its properties are studied. We call it hierarchical product, because of the strong (connectedness) hierarchy of the vertices in the resulting graphs. In fact, the obtained graphs turn out to be subgraphs of the cartesian product of the corresponding factors. Some well-known properties of the cartesian product, such as reduced mean distance and diameter, simple routing algorithms and some optimal communication protocols are inherited by the hierarchical product. We also address the study of some algebraic properties of the hierarchical product of two or more graphs. In particular, the spectrum of the binary hypertree Tm (which is the hierarchical product of several copies of the complete graph on two vertices) is fully characterized; turning out to be an interesting example of graph with all its eigenvalues distinct. Finally, some natural generalizations of the hierarchic product are proposed.
publishDate 2009
dc.date.none.fl_str_mv 2009
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://doi.org/10.1016/j.dam.2008.04.018
https://hdl.handle.net/10459.1/463314
url https://doi.org/10.1016/j.dam.2008.04.018
https://hdl.handle.net/10459.1/463314
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió preprint del document publicat a: https://doi.org/10.1016/j.dam.2008.04.018
Discrete Applied Mathematics, 2009, vol. 157, p. 36-48
Discrete Applied Mathematics
dc.rights.none.fl_str_mv cc-by-nc-nd, (c) Elsevier, 2009
Attribution-NonCommercial-NoDerivatives 4.0 International
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/
rights_invalid_str_mv cc-by-nc-nd, (c) Elsevier, 2009
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.81155

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