New results on metric-locating-dominating sets of graphs

A dominating set S of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distanc es from the elements of S , and the minimum cardinality of such a set is called the metri c-location- domination number. In this paper, we undertake a study that, in...

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Detalles Bibliográficos
Autores: Hernando Martín, María del Carmen|||0000-0002-3864-6566, Mora Giné, Mercè|||0000-0001-6923-0320, González, Antonio
Tipo de recurso: informe técnico
Fecha de publicación:2016
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:2117/96709
Acceso en línea:https://hdl.handle.net/2117/96709
Access Level:acceso abierto
Palabra clave:Graph theory
Number theory
metric-locating-dominating set
resolving set
dominati ng set
locating- dominating set
doubly resolving set
Grafs, Teoria de
Nombres, Teoria dels
Àrees temàtiques de la UPC::Matemàtiques i estadística
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network_acronym_str ES
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repository_id_str
spelling New results on metric-locating-dominating sets of graphsHernando Martín, María del Carmen|||0000-0002-3864-6566Mora Giné, Mercè|||0000-0001-6923-0320González, AntonioGraph theoryNumber theorymetric-locating-dominating setresolving setdominati ng setlocating- dominating setdoubly resolving setGrafs, Teoria deNombres, Teoria delsÀrees temàtiques de la UPC::Matemàtiques i estadísticaA dominating set S of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distanc es from the elements of S , and the minimum cardinality of such a set is called the metri c-location- domination number. In this paper, we undertake a study that, in general graphs and specific families, relates metric-locating-dominatin g sets to other special sets: resolving sets, dominating sets, locating-dominating set s and doubly resolving sets. We first characterize classes of trees according to cer tain relationships between their metric-location-domination number and thei r metric dimension and domination number. Then, we show different methods to tran sform metric- locating-dominating sets into locating-dominating sets a nd doubly resolving sets. Our methods produce new bounds on the minimum cardinalities of all those sets, some of them involving parameters that have not been related so far20162016-04-1320162016-11-16reporthttp://purl.org/coar/resource_type/c_93fcVoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/2117/96709reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/967092026-05-27T15:37:01Z
dc.title.none.fl_str_mv New results on metric-locating-dominating sets of graphs
title New results on metric-locating-dominating sets of graphs
spellingShingle New results on metric-locating-dominating sets of graphs
Hernando Martín, María del Carmen|||0000-0002-3864-6566
Graph theory
Number theory
metric-locating-dominating set
resolving set
dominati ng set
locating- dominating set
doubly resolving set
Grafs, Teoria de
Nombres, Teoria dels
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short New results on metric-locating-dominating sets of graphs
title_full New results on metric-locating-dominating sets of graphs
title_fullStr New results on metric-locating-dominating sets of graphs
title_full_unstemmed New results on metric-locating-dominating sets of graphs
title_sort New results on metric-locating-dominating sets of graphs
dc.creator.none.fl_str_mv Hernando Martín, María del Carmen|||0000-0002-3864-6566
Mora Giné, Mercè|||0000-0001-6923-0320
González, Antonio
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
González, Antonio
author_role author
author2 Mora Giné, Mercè|||0000-0001-6923-0320
González, Antonio
author2_role author
author
dc.subject.none.fl_str_mv Graph theory
Number theory
metric-locating-dominating set
resolving set
dominati ng set
locating- dominating set
doubly resolving set
Grafs, Teoria de
Nombres, Teoria dels
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Graph theory
Number theory
metric-locating-dominating set
resolving set
dominati ng set
locating- dominating set
doubly resolving set
Grafs, Teoria de
Nombres, Teoria dels
Àrees temàtiques de la UPC::Matemàtiques i estadística
description A dominating set S of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distanc es from the elements of S , and the minimum cardinality of such a set is called the metri c-location- domination number. In this paper, we undertake a study that, in general graphs and specific families, relates metric-locating-dominatin g sets to other special sets: resolving sets, dominating sets, locating-dominating set s and doubly resolving sets. We first characterize classes of trees according to cer tain relationships between their metric-location-domination number and thei r metric dimension and domination number. Then, we show different methods to tran sform metric- locating-dominating sets into locating-dominating sets a nd doubly resolving sets. Our methods produce new bounds on the minimum cardinalities of all those sets, some of them involving parameters that have not been related so far
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-04-13
2016
2016-11-16
dc.type.none.fl_str_mv report
http://purl.org/coar/resource_type/c_93fc
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/96709
url https://hdl.handle.net/2117/96709
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2

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

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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