Neighbor-locating colorings in graphs

Document typeExternal research report
Defense date2018-06-29
Rights accessOpen Access
European Commission's projectCONNECT - Combinatorics of Networks and Computation (EC-H2020-734922)
Abstract
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
CitationHernando, M., Mora, M., Pelayo, I. M., Alcón, L., Gutierrez, M. "Neighbor-locating colorings in graphs". 2018.
URL other repositoryhttps://arxiv.org/pdf/1806.11465.pdf
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