Neighbor-locating colorings in graphs

A k -coloring of a graph G is a k -partition ¿ = { S 1 ,...,S k } of V ( G ) into independent sets, called colors . A k -coloring is called neighbor-locating if for every pair of vertices u,v belonging to the same color S i , the set of colors of the neighborhood of u is different from the set of co...

Full description

Bibliographic Details
Authors: Hernando Martín, María del Carmen|||0000-0002-3864-6566, Mora Giné, Mercè|||0000-0001-6923-0320, Pelayo Melero, Ignacio Manuel|||0000-0002-6523-0611, Alcón, Liliana, Gutierrez, Marisa
Format: report
Publication Date:2018
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/121239
Online Access:https://hdl.handle.net/2117/121239
Access Level:Open access
Keyword:Graph theory
coloring
domination
location
vertex partition
neighbor-locating coloring
Grafs, Teoria de
Àrees temàtiques de la UPC::Matemàtiques i estadística
Description
Summary:A k -coloring of a graph G is a k -partition ¿ = { S 1 ,...,S k } of V ( G ) into independent sets, called colors . A k -coloring is called neighbor-locating if for every pair of vertices u,v belonging to the same color S i , the set of colors of the neighborhood of u is different from the set of colors of the neighborhood of v . The neighbor-locating chromatic number ¿ NL ( G ) is the minimum cardinality of a neighbor-locating coloring of G . We establish some tight bounds for the neighbor-locating chromatic number of a graph, in terms of its order, maximum degree and independence number. We determine all connected graphs of order n = 5 with neighbor-locating chromatic number n or n - 1. We examine the neighbor-locating chromatic number for two graph operations: join and disjoint union, and also for two graph families: split graphs and Mycielski graphs