Neighbor-Locating Colorings in Graphs
Liliana Alcon, Marisa Gutierrez, Carmen Hernando, Merce Mora, Ignacio, M. Pelayo

TL;DR
This paper introduces the neighbor-locating chromatic number, a new graph coloring parameter, and establishes bounds, characterizations, and behavior under graph operations for various graph classes.
Contribution
It defines the neighbor-locating chromatic number, provides tight bounds, characterizes extremal graphs, and analyzes its behavior under join, union, and specific graph families.
Findings
Established tight bounds in terms of graph parameters.
Characterized all graphs with maximum neighbor-locating chromatic number.
Analyzed the parameter for join, union, split, and Mycielski graphs.
Abstract
A -coloring of a graph is a -partition of into independent sets, called \emph{colors}. A -coloring is called \emph{neighbor-locating} if for every pair of vertices belonging to the same color , the set of colors of the neighborhood of is different from the set of colors of the neighborhood of . The neighbor-locating chromatic number is the minimum cardinality of a neighbor-locating coloring of . 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 with neighbor-locating chromatic number or . We examine the neighbor-locating chromatic number for two graph operations: join and disjoint union, and also for two graph families: split graphs and…
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Taxonomy
TopicsGraph Labeling and Dimension Problems
