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 orde...
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.
Citation
Alcón, L. [et al.]. Neighbor-locating colorings in graphs. "Theoretical computer science", 2 Febrer 2020, vol. 806, p. 144-155.