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Neighbor-locating colorings in graphs

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10.1016/j.tcs.2019.01.039
 
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Alcón, Liliana
Gutierrez, Marisa
Hernando Martín, María del CarmenMés informacióMés informacióMés informació
Mora Giné, MercèMés informacióMés informacióMés informació
Pelayo Melero, Ignacio ManuelMés informacióMés informacióMés informació
Document typeArticle
Defense date2020-02-02
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
ProjectCONNECT - Combinatorics of Networks and Computation (EC-H2020-734922)
Abstract
A k-coloring of a graph G is a k-partition of into independent sets, called colors. A k-coloring is called neighbor-locating if for every pair of vertices belonging to the same color , 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 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 with neighbor-locating chromatic number n 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 Mycielski graphs.
CitationAlcón, L. [et al.]. Neighbor-locating colorings in graphs. "Theoretical computer science", 2 Febrer 2020, vol. 806, p. 144-155. 
URIhttp://hdl.handle.net/2117/335501
DOI10.1016/j.tcs.2019.01.039
ISSN0304-3975
Publisher versionhttps://www.sciencedirect.com/science/article/pii/S0304397519300805
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  • DCG - Discrete and Combinatorial Geometry - Articles de revista [29]
  • Departament de Matemàtiques - Articles de revista [2.973]
  • COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions - Articles de revista [290]
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