The difference between the metric dimension and the determining number of a graph

We study the maximum value of the difference between the metric dimension and the determining number of a graph as a function of its order. We develop a technique that uses functions related to locating-dominating sets to obtain lower and upper bounds on that maximum, and exact computations when res...

Full description

Bibliographic Details
Authors: Garijo Royo, Delia, González Herrera, Antonio, Márquez Pérez, Alberto
Format: article
Status:Published version
Publication Date:2014
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/38838
Online Access:http://hdl.handle.net/11441/38838
https://doi.org/10.1016/j.amc.2014.10.034
Access Level:Open access
Keyword:Resolving set
Metric dimension
Determining set
Determining number
Locating-dominating set
Locating-domination number
id ES_15d2da4943fb9ab9ed8fa04018e45074
oai_identifier_str oai:idus.us.es:11441/38838
network_acronym_str ES
network_name_str España
repository_id_str
spelling The difference between the metric dimension and the determining number of a graphGarijo Royo, DeliaGonzález Herrera, AntonioMárquez Pérez, AlbertoResolving setMetric dimensionDetermining setDetermining numberLocating-dominating setLocating-domination numberWe study the maximum value of the difference between the metric dimension and the determining number of a graph as a function of its order. We develop a technique that uses functions related to locating-dominating sets to obtain lower and upper bounds on that maximum, and exact computations when restricting to some specific families of graphs. Our approach requires very diverse tools and connections with well-known objects in graph theory; among them: a classical result in graph domination by Ore, a Ramsey-type result by Erdős and Szekeres, a polynomial time algorithm to compute distinguishing sets and determining sets of twin-free graphs, k-dominating sets, and matchings.Matemática Aplicada I2014info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/38838https://doi.org/10.1016/j.amc.2014.10.034reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésApplied Mathematics and Computation, 249, 487-501.info:eu-repo/semantics/openAccessoai:idus.us.es:11441/388382026-06-17T12:51:07Z
dc.title.none.fl_str_mv The difference between the metric dimension and the determining number of a graph
title The difference between the metric dimension and the determining number of a graph
spellingShingle The difference between the metric dimension and the determining number of a graph
Garijo Royo, Delia
Resolving set
Metric dimension
Determining set
Determining number
Locating-dominating set
Locating-domination number
title_short The difference between the metric dimension and the determining number of a graph
title_full The difference between the metric dimension and the determining number of a graph
title_fullStr The difference between the metric dimension and the determining number of a graph
title_full_unstemmed The difference between the metric dimension and the determining number of a graph
title_sort The difference between the metric dimension and the determining number of a graph
dc.creator.none.fl_str_mv Garijo Royo, Delia
González Herrera, Antonio
Márquez Pérez, Alberto
author Garijo Royo, Delia
author_facet Garijo Royo, Delia
González Herrera, Antonio
Márquez Pérez, Alberto
author_role author
author2 González Herrera, Antonio
Márquez Pérez, Alberto
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
dc.subject.none.fl_str_mv Resolving set
Metric dimension
Determining set
Determining number
Locating-dominating set
Locating-domination number
topic Resolving set
Metric dimension
Determining set
Determining number
Locating-dominating set
Locating-domination number
description We study the maximum value of the difference between the metric dimension and the determining number of a graph as a function of its order. We develop a technique that uses functions related to locating-dominating sets to obtain lower and upper bounds on that maximum, and exact computations when restricting to some specific families of graphs. Our approach requires very diverse tools and connections with well-known objects in graph theory; among them: a classical result in graph domination by Ore, a Ramsey-type result by Erdős and Szekeres, a polynomial time algorithm to compute distinguishing sets and determining sets of twin-free graphs, k-dominating sets, and matchings.
publishDate 2014
dc.date.none.fl_str_mv 2014
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 http://hdl.handle.net/11441/38838
https://doi.org/10.1016/j.amc.2014.10.034
url http://hdl.handle.net/11441/38838
https://doi.org/10.1016/j.amc.2014.10.034
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Applied Mathematics and Computation, 249, 487-501.
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.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
_version_ 1869403817558147072
score 15.301629

Similar Items