Neighbor-locating coloring: graph operations and extremal cardinalities
A k–coloring of a graph G = ( V , E ) is a k-partition II = { S 1 , … , S k } 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 S i , the set of colors of the neighborhood of u is different from the set...
Guardado en:
| Autores principales: | , , , , |
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| Formato: | Articulo Preprint |
| Lenguaje: | Inglés |
| Publicado: |
2018
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/125581 |
| Aporte de: |
| Sumario: | A k–coloring of a graph G = ( V , E ) is a k-partition II = { S 1 , … , S k } 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 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, χ NL (G) , 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 n ≥ 3 with neighbor-locating chromatic number equal either to n or to n − 1 and determine the neighbor-locating chromatic number of split graphs. |
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