Neighbor-locating coloring: graph operations and extremal cardinalities
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A k–coloring of a graph is a k-partition of V 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 , 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. In this paper, we examine the neighbor-locating chromatic number for various graph operations: the join, the disjoint union and Cartesian product. We also characterize all connected graphs of order with neighbor-locating chromatic number equal either to n or to and determine the neighbor-locating chromatic number of split graphs.
© 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
CitationHernando, M., Mora, M., Pelayo, I. M. Neighbor-locating coloring: graph operations and extremal cardinalities. "Electronic notes in discrete mathematics", 1 Juliol 2018, vol. 68, núm. July 2018, p. 131-136.
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