Resolving dominating partitions in graphs

A partition ¿ ={S1,...,Sk}of the vertex set of a connected graphGis called aresolvingpartitionofGif for every pair of verticesuandv,d(u,Sj)6=d(v,Sj), for some partSj. Thepartition dimensionßp(G) is the minimum cardinality of a resolving partition ofG. A resolvingpartition ¿ is calledresolving domina...

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Detalles Bibliográficos
Autores: Hernando Martín, María del Carmen|||0000-0002-3864-6566, Mora Giné, Mercè|||0000-0001-6923-0320, Pelayo Melero, Ignacio Manuel|||0000-0002-6523-0611
Tipo de recurso: artículo
Fecha de publicación:2019
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:2117/171094
Acceso en línea:https://hdl.handle.net/2117/171094
https://dx.doi.org/10.1016/j.dam.2018.12.001
Access Level:acceso abierto
Palabra clave:Graph theory
Resolving partition
Resolving dominating partition
Metric location
Resolving domination
Partition dimension
Dominating partition dimension
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística
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oai_identifier_str oai:upcommons.upc.edu:2117/171094
network_acronym_str ES
network_name_str España
repository_id_str
spelling Resolving dominating partitions in graphsHernando Martín, María del Carmen|||0000-0002-3864-6566Mora Giné, Mercè|||0000-0001-6923-0320Pelayo Melero, Ignacio Manuel|||0000-0002-6523-0611Graph theoryResolving partitionResolving dominating partitionMetric locationResolving dominationPartition dimensionDominating partition dimensionGrafs, Teoria deClassificació AMS::05 Combinatorics::05C Graph theoryÀrees temàtiques de la UPC::Matemàtiques i estadísticaA partition ¿ ={S1,...,Sk}of the vertex set of a connected graphGis called aresolvingpartitionofGif for every pair of verticesuandv,d(u,Sj)6=d(v,Sj), for some partSj. Thepartition dimensionßp(G) is the minimum cardinality of a resolving partition ofG. A resolvingpartition ¿ is calledresolving dominatingif for every vertexvofG,d(v,Sj) = 1, for some partSjof ¿. Thedominating partition dimension¿p(G) is the minimum cardinality of a resolvingdominating partition ofG.In this paper we show, among other results, thatßp(G)=¿p(G)=ßp(G) + 1. We alsocharacterize all connected graphs of ordern=7 satisfying any of the following conditions:¿p(G) =n,¿p(G) =n-1,¿p(G) =n-2 andßp(G) =n-2. Finally, we present some tightNordhaus-Gaddum bounds for both the partition dimensionßp(G) and the dominating partitiondimension¿p(G).Peer Reviewed20192019-01-0120192019-10-30journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/171094https://dx.doi.org/10.1016/j.dam.2018.12.001reponame: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:2117/1710942026-05-27T15:37:01Z
dc.title.none.fl_str_mv Resolving dominating partitions in graphs
title Resolving dominating partitions in graphs
spellingShingle Resolving dominating partitions in graphs
Hernando Martín, María del Carmen|||0000-0002-3864-6566
Graph theory
Resolving partition
Resolving dominating partition
Metric location
Resolving domination
Partition dimension
Dominating partition dimension
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short Resolving dominating partitions in graphs
title_full Resolving dominating partitions in graphs
title_fullStr Resolving dominating partitions in graphs
title_full_unstemmed Resolving dominating partitions in graphs
title_sort Resolving dominating partitions in graphs
dc.creator.none.fl_str_mv Hernando Martín, María del Carmen|||0000-0002-3864-6566
Mora Giné, Mercè|||0000-0001-6923-0320
Pelayo Melero, Ignacio Manuel|||0000-0002-6523-0611
author Hernando Martín, María del Carmen|||0000-0002-3864-6566
author_facet Hernando Martín, María del Carmen|||0000-0002-3864-6566
Mora Giné, Mercè|||0000-0001-6923-0320
Pelayo Melero, Ignacio Manuel|||0000-0002-6523-0611
author_role author
author2 Mora Giné, Mercè|||0000-0001-6923-0320
Pelayo Melero, Ignacio Manuel|||0000-0002-6523-0611
author2_role author
author
dc.subject.none.fl_str_mv Graph theory
Resolving partition
Resolving dominating partition
Metric location
Resolving domination
Partition dimension
Dominating partition dimension
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Graph theory
Resolving partition
Resolving dominating partition
Metric location
Resolving domination
Partition dimension
Dominating partition dimension
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística
description A partition ¿ ={S1,...,Sk}of the vertex set of a connected graphGis called aresolvingpartitionofGif for every pair of verticesuandv,d(u,Sj)6=d(v,Sj), for some partSj. Thepartition dimensionßp(G) is the minimum cardinality of a resolving partition ofG. A resolvingpartition ¿ is calledresolving dominatingif for every vertexvofG,d(v,Sj) = 1, for some partSjof ¿. Thedominating partition dimension¿p(G) is the minimum cardinality of a resolvingdominating partition ofG.In this paper we show, among other results, thatßp(G)=¿p(G)=ßp(G) + 1. We alsocharacterize all connected graphs of ordern=7 satisfying any of the following conditions:¿p(G) =n,¿p(G) =n-1,¿p(G) =n-2 andßp(G) =n-2. Finally, we present some tightNordhaus-Gaddum bounds for both the partition dimensionßp(G) and the dominating partitiondimension¿p(G).
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01
2019
2019-10-30
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/2117/171094
https://dx.doi.org/10.1016/j.dam.2018.12.001
url https://hdl.handle.net/2117/171094
https://dx.doi.org/10.1016/j.dam.2018.12.001
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 15.301603

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