On perfect and quasiperfect dominations in graphs

A subset S ¿ V in a graph G = ( V , E ) is a k -quasiperfect dominating set (for k = 1) if every vertex not in S is adjacent to at least one and at most k vertices in S . The cardinality of a minimum k -quasiperfect dominating set in G is denoted by ¿ 1 k ( G ). Those sets were first introduced by C...

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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, Cáceres, José, Puertas, M. Luz
Tipo de recurso: artículo
Fecha de publicación:2017
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:2117/104244
Acceso en línea:https://hdl.handle.net/2117/104244
https://dx.doi.org/10.2298 / FIL1702413C
Access Level:acceso abierto
Palabra clave:Graph theory
Domination
perfect domination
quasiperfect domination
claw-free graphs
cograph
Grafs, Teoria de
Geometria discreta
Àrees temàtiques de la UPC::Matemàtiques i estadística
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spelling On perfect and quasiperfect dominations in graphsHernando Martín, María del Carmen|||0000-0002-3864-6566Mora Giné, Mercè|||0000-0001-6923-0320Pelayo Melero, Ignacio Manuel|||0000-0002-6523-0611Cáceres, JoséPuertas, M. LuzGraph theoryDominationperfect dominationquasiperfect dominationclaw-free graphscographGrafs, Teoria deGeometria discretaÀrees temàtiques de la UPC::Matemàtiques i estadísticaA subset S ¿ V in a graph G = ( V , E ) is a k -quasiperfect dominating set (for k = 1) if every vertex not in S is adjacent to at least one and at most k vertices in S . The cardinality of a minimum k -quasiperfect dominating set in G is denoted by ¿ 1 k ( G ). Those sets were first introduced by Chellali et al. (2013) as a generalization of the perfect domination concept and allow us to construct a decreasing chain of quasiperfect dominating numbers n = ¿ 11 ( G ) = ¿ 12 ( G ) = ... = ¿ 1 ¿ ( G ) = ¿ ( G ) in order to indicate how far is G from being perfectly dominated. In this paper we study properties, existence and realization of graphs for which the chain is short, that is, ¿ 12 ( G ) = ¿ ( G ). Among them, one can find cographs, claw-free graphs and graphs with extremal values of ¿ ( G ).20172017-02-2720172017-05-10journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/104244https://dx.doi.org/10.2298 / FIL1702413Creponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen 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:2117/1042442026-05-27T15:37:01Z
dc.title.none.fl_str_mv On perfect and quasiperfect dominations in graphs
title On perfect and quasiperfect dominations in graphs
spellingShingle On perfect and quasiperfect dominations in graphs
Hernando Martín, María del Carmen|||0000-0002-3864-6566
Graph theory
Domination
perfect domination
quasiperfect domination
claw-free graphs
cograph
Grafs, Teoria de
Geometria discreta
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short On perfect and quasiperfect dominations in graphs
title_full On perfect and quasiperfect dominations in graphs
title_fullStr On perfect and quasiperfect dominations in graphs
title_full_unstemmed On perfect and quasiperfect dominations in graphs
title_sort On perfect and quasiperfect dominations 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
Cáceres, José
Puertas, M. Luz
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
Cáceres, José
Puertas, M. Luz
author_role author
author2 Mora Giné, Mercè|||0000-0001-6923-0320
Pelayo Melero, Ignacio Manuel|||0000-0002-6523-0611
Cáceres, José
Puertas, M. Luz
author2_role author
author
author
author
dc.subject.none.fl_str_mv Graph theory
Domination
perfect domination
quasiperfect domination
claw-free graphs
cograph
Grafs, Teoria de
Geometria discreta
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Graph theory
Domination
perfect domination
quasiperfect domination
claw-free graphs
cograph
Grafs, Teoria de
Geometria discreta
Àrees temàtiques de la UPC::Matemàtiques i estadística
description A subset S ¿ V in a graph G = ( V , E ) is a k -quasiperfect dominating set (for k = 1) if every vertex not in S is adjacent to at least one and at most k vertices in S . The cardinality of a minimum k -quasiperfect dominating set in G is denoted by ¿ 1 k ( G ). Those sets were first introduced by Chellali et al. (2013) as a generalization of the perfect domination concept and allow us to construct a decreasing chain of quasiperfect dominating numbers n = ¿ 11 ( G ) = ¿ 12 ( G ) = ... = ¿ 1 ¿ ( G ) = ¿ ( G ) in order to indicate how far is G from being perfectly dominated. In this paper we study properties, existence and realization of graphs for which the chain is short, that is, ¿ 12 ( G ) = ¿ ( G ). Among them, one can find cographs, claw-free graphs and graphs with extremal values of ¿ ( G ).
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-02-27
2017
2017-05-10
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/104244
https://dx.doi.org/10.2298 / FIL1702413C
url https://hdl.handle.net/2117/104244
https://dx.doi.org/10.2298 / FIL1702413C
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
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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