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

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 neighbo...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Alcón, Liliana Graciela, Gutiérrez, Marisa, Hernando, Carmen, Mora, Mercè, Pelayo, Ignacio M.
Formato:	Articulo
Lenguaje:	Inglés
Publicado:	2023
Materias:	Ciencias Exactas Matemática coloring location neighbor-locating coloring unicyclic graph tree
Acceso en línea:	http://sedici.unlp.edu.ar/handle/10915/162603
Aporte de:	SEDICI (UNLP) de Universidad Nacional de La Plata

id	I19-R120-10915-162603
record_format	dspace
spelling	I19-R120-10915-1626032024-02-09T20:50:59Z http://sedici.unlp.edu.ar/handle/10915/162603 The neighbor-locating-chromatic number of trees and unicyclic graphs Alcón, Liliana Graciela Gutiérrez, Marisa Hernando, Carmen Mora, Mercè Pelayo, Ignacio M. 2023 2024-02-09T18:42:17Z en Ciencias Exactas Matemática coloring location neighbor-locating coloring unicyclic graph tree 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 Articulo Articulo http://creativecommons.org/licenses/by-nc-nd/4.0/ Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) application/pdf 659-675
institution	Universidad Nacional de La Plata
institution_str	I-19
repository_str	R-120
collection	SEDICI (UNLP)
language	Inglés
topic	Ciencias Exactas Matemática coloring location neighbor-locating coloring unicyclic graph tree
spellingShingle	Ciencias Exactas Matemática coloring location neighbor-locating coloring unicyclic graph tree Alcón, Liliana Graciela Gutiérrez, Marisa Hernando, Carmen Mora, Mercè Pelayo, Ignacio M. The neighbor-locating-chromatic number of trees and unicyclic graphs
topic_facet	Ciencias Exactas Matemática coloring location neighbor-locating coloring unicyclic graph tree
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.
format	Articulo Articulo
author	Alcón, Liliana Graciela Gutiérrez, Marisa Hernando, Carmen Mora, Mercè Pelayo, Ignacio M.
author_facet	Alcón, Liliana Graciela Gutiérrez, Marisa Hernando, Carmen Mora, Mercè Pelayo, Ignacio M.
author_sort	Alcón, Liliana Graciela
title	The neighbor-locating-chromatic number of trees and unicyclic graphs
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	neighbor-locating-chromatic number of trees and unicyclic graphs
publishDate	2023
url	http://sedici.unlp.edu.ar/handle/10915/162603
work_keys_str_mv	AT alconlilianagraciela theneighborlocatingchromaticnumberoftreesandunicyclicgraphs AT gutierrezmarisa theneighborlocatingchromaticnumberoftreesandunicyclicgraphs AT hernandocarmen theneighborlocatingchromaticnumberoftreesandunicyclicgraphs AT moramerce theneighborlocatingchromaticnumberoftreesandunicyclicgraphs AT pelayoignaciom theneighborlocatingchromaticnumberoftreesandunicyclicgraphs AT alconlilianagraciela neighborlocatingchromaticnumberoftreesandunicyclicgraphs AT gutierrezmarisa neighborlocatingchromaticnumberoftreesandunicyclicgraphs AT hernandocarmen neighborlocatingchromaticnumberoftreesandunicyclicgraphs AT moramerce neighborlocatingchromaticnumberoftreesandunicyclicgraphs AT pelayoignaciom neighborlocatingchromaticnumberoftreesandunicyclicgraphs
_version_	1807222411471355904

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

Ejemplares similares