The Equidistant Dimension of Graphs

Asubset S of vertices of a connected graphG is a distance-equalizer set if for every two distinct vertices x, y ∈ V(G)\S there is a vertex w ∈ S such that the distances from x and y to w are the same. The equidistant dimension of G is the minimum cardinality of a distance-equalizer set of G. This pa...

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Detalles Bibliográficos
Autores: González Herrera, Antonio, Hernando, C., Mora, M.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/138683
Acceso en línea:https://hdl.handle.net/11441/138683
https://doi.org/10.1007/s40840-022-01295-z
Access Level:acceso abierto
Palabra clave:Distance-equalizer set
Equidistant dimension
Resolving set
Doubly resolving set
Metric dimension
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spelling The Equidistant Dimension of GraphsGonzález Herrera, AntonioHernando, C.Mora, M.Distance-equalizer setEquidistant dimensionResolving setDoubly resolving setMetric dimensionAsubset S of vertices of a connected graphG is a distance-equalizer set if for every two distinct vertices x, y ∈ V(G)\S there is a vertex w ∈ S such that the distances from x and y to w are the same. The equidistant dimension of G is the minimum cardinality of a distance-equalizer set of G. This paper is devoted to introduce this parameter and explore its properties and applications to other mathematical problems, not necessarily in the context of graph theory. Concretely, we first establish some bounds concerning the order, the maximum degree, the clique number, and the independence number, and characterize all graphs attaining some extremal values. We then study the equidistant dimension of several families of graphs (complete and complete multipartite graphs, bistars, paths, cycles, and Johnson graphs), proving that, in the case of paths and cycles, this parameter is related to 3-AP-free sets. Subsequently, we show the usefulness of distance-equalizer sets for constructing doubly resolving sets.SpringerDidáctica de las MatemáticasFQM-226: Educación matemáticaEuropean Union’s Horizon 2020Ministerio de Ciencia e Innovación2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/138683https://doi.org/10.1007/s40840-022-01295-zreponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésBulletin of the malaysian mathematical sciences society, 45 (4), 1757-1775.734922 - CONNECTPID2019-104129GB-I00/AEI/10.13039/501100011033http://doi.org/10.1007/s40840-022-01295-zinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/1386832026-06-17T12:51:07Z
dc.title.none.fl_str_mv The Equidistant Dimension of Graphs
title The Equidistant Dimension of Graphs
spellingShingle The Equidistant Dimension of Graphs
González Herrera, Antonio
Distance-equalizer set
Equidistant dimension
Resolving set
Doubly resolving set
Metric dimension
title_short The Equidistant Dimension of Graphs
title_full The Equidistant Dimension of Graphs
title_fullStr The Equidistant Dimension of Graphs
title_full_unstemmed The Equidistant Dimension of Graphs
title_sort The Equidistant Dimension of Graphs
dc.creator.none.fl_str_mv González Herrera, Antonio
Hernando, C.
Mora, M.
author González Herrera, Antonio
author_facet González Herrera, Antonio
Hernando, C.
Mora, M.
author_role author
author2 Hernando, C.
Mora, M.
author2_role author
author
dc.contributor.none.fl_str_mv Didáctica de las Matemáticas
FQM-226: Educación matemática
European Union’s Horizon 2020
Ministerio de Ciencia e Innovación
dc.subject.none.fl_str_mv Distance-equalizer set
Equidistant dimension
Resolving set
Doubly resolving set
Metric dimension
topic Distance-equalizer set
Equidistant dimension
Resolving set
Doubly resolving set
Metric dimension
description Asubset S of vertices of a connected graphG is a distance-equalizer set if for every two distinct vertices x, y ∈ V(G)\S there is a vertex w ∈ S such that the distances from x and y to w are the same. The equidistant dimension of G is the minimum cardinality of a distance-equalizer set of G. This paper is devoted to introduce this parameter and explore its properties and applications to other mathematical problems, not necessarily in the context of graph theory. Concretely, we first establish some bounds concerning the order, the maximum degree, the clique number, and the independence number, and characterize all graphs attaining some extremal values. We then study the equidistant dimension of several families of graphs (complete and complete multipartite graphs, bistars, paths, cycles, and Johnson graphs), proving that, in the case of paths and cycles, this parameter is related to 3-AP-free sets. Subsequently, we show the usefulness of distance-equalizer sets for constructing doubly resolving sets.
publishDate 2022
dc.date.none.fl_str_mv 2022
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://hdl.handle.net/11441/138683
https://doi.org/10.1007/s40840-022-01295-z
url https://hdl.handle.net/11441/138683
https://doi.org/10.1007/s40840-022-01295-z
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Bulletin of the malaysian mathematical sciences society, 45 (4), 1757-1775.
734922 - CONNECT
PID2019-104129GB-I00/AEI/10.13039/501100011033
http://doi.org/10.1007/s40840-022-01295-z
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301629

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