The neighbor-locating-chromatic number of trees and unicyclic graphs

Autores
Alcón, Liliana Graciela; Gutiérrez, Marisa; Hernando, Carmen; Mora, Mercè; Pelayo, Ignacio M.
Año de publicación
2023
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A k-coloring of a graph is neighbor-locating if any two vertices with the same color can be distinguished by the colors of their respective neighbors, that is, the sets of colors of their neighborhoods are different. The neighbor- locating chromatic number χNL(G) is the minimum k such that a neighbor- locating k-coloring of G exists. In this paper, we give upper and lower bounds on the neighbor-locating chromatic number in terms of the order and the degree of the vertices for unicyclic graphs and trees. We also obtain tight upper bounds on the order of trees and unicyclic graphs in terms of the neighbor-locating chromatic number. Further partial results for trees are also established.
Facultad de Ciencias Exactas
Departamento de Matemática
Materia
Ciencias Exactas
Matemática
coloring
location
neighbor-locating coloring
unicyclic graph
tree
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-nd/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/162603
Acceder
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network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling The neighbor-locating-chromatic number of trees and unicyclic graphsAlcón, Liliana GracielaGutiérrez, MarisaHernando, CarmenMora, MercèPelayo, Ignacio M.Ciencias ExactasMatemáticacoloringlocationneighbor-locating coloringunicyclic graphtreeA k-coloring of a graph is neighbor-locating if any two vertices with the same color can be distinguished by the colors of their respective neighbors, that is, the sets of colors of their neighborhoods are different. The neighbor- locating chromatic number χNL(G) is the minimum k such that a neighbor- locating k-coloring of G exists. In this paper, we give upper and lower bounds on the neighbor-locating chromatic number in terms of the order and the degree of the vertices for unicyclic graphs and trees. We also obtain tight upper bounds on the order of trees and unicyclic graphs in terms of the neighbor-locating chromatic number. Further partial results for trees are also established.Facultad de Ciencias ExactasDepartamento de Matemática2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf659-675http://sedici.unlp.edu.ar/handle/10915/162603enginfo:eu-repo/semantics/altIdentifier/issn/1234-3099info:eu-repo/semantics/altIdentifier/issn/2083-5892info:eu-repo/semantics/altIdentifier/doi/10.7151/dmgt.2392info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:42:46Zoai:sedici.unlp.edu.ar:10915/162603Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:42:46.269SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv The neighbor-locating-chromatic number of trees and unicyclic graphs
title The neighbor-locating-chromatic number of trees and unicyclic graphs
spellingShingle The neighbor-locating-chromatic number of trees and unicyclic graphs
Alcón, Liliana Graciela
Ciencias Exactas
Matemática
coloring
location
neighbor-locating coloring
unicyclic graph
tree
title_short The neighbor-locating-chromatic number of trees and unicyclic graphs
title_full The neighbor-locating-chromatic number of trees and unicyclic graphs
title_fullStr The neighbor-locating-chromatic number of trees and unicyclic graphs
title_full_unstemmed The neighbor-locating-chromatic number of trees and unicyclic graphs
title_sort The neighbor-locating-chromatic number of trees and unicyclic graphs
dc.creator.none.fl_str_mv Alcón, Liliana Graciela
Gutiérrez, Marisa
Hernando, Carmen
Mora, Mercè
Pelayo, Ignacio M.
author Alcón, Liliana Graciela
author_facet Alcón, Liliana Graciela
Gutiérrez, Marisa
Hernando, Carmen
Mora, Mercè
Pelayo, Ignacio M.
author_role author
author2 Gutiérrez, Marisa
Hernando, Carmen
Mora, Mercè
Pelayo, Ignacio M.
author2_role author
author
author
author
dc.subject.none.fl_str_mv Ciencias Exactas
Matemática
coloring
location
neighbor-locating coloring
unicyclic graph
tree
topic Ciencias Exactas
Matemática
coloring
location
neighbor-locating coloring
unicyclic graph
tree
dc.description.none.fl_txt_mv A k-coloring of a graph is neighbor-locating if any two vertices with the same color can be distinguished by the colors of their respective neighbors, that is, the sets of colors of their neighborhoods are different. The neighbor- locating chromatic number χNL(G) is the minimum k such that a neighbor- locating k-coloring of G exists. In this paper, we give upper and lower bounds on the neighbor-locating chromatic number in terms of the order and the degree of the vertices for unicyclic graphs and trees. We also obtain tight upper bounds on the order of trees and unicyclic graphs in terms of the neighbor-locating chromatic number. Further partial results for trees are also established.
Facultad de Ciencias Exactas
Departamento de Matemática
description A k-coloring of a graph is neighbor-locating if any two vertices with the same color can be distinguished by the colors of their respective neighbors, that is, the sets of colors of their neighborhoods are different. The neighbor- locating chromatic number χNL(G) is the minimum k such that a neighbor- locating k-coloring of G exists. In this paper, we give upper and lower bounds on the neighbor-locating chromatic number in terms of the order and the degree of the vertices for unicyclic graphs and trees. We also obtain tight upper bounds on the order of trees and unicyclic graphs in terms of the neighbor-locating chromatic number. Further partial results for trees are also established.
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/162603
url http://sedici.unlp.edu.ar/handle/10915/162603
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/1234-3099
info:eu-repo/semantics/altIdentifier/issn/2083-5892
info:eu-repo/semantics/altIdentifier/doi/10.7151/dmgt.2392
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
dc.format.none.fl_str_mv application/pdf
659-675
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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