Geodesic
Packing Coloring of Some Undirected and Oriented Coronae Graphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 665-690

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The packing chromatic number χρ(G) of a graph G is the smallest integer k such that its set of vertices V(G) can be partitioned into k disjoint subsets V1, . . ., Vk, in such a way that every two distinct vertices in Vi are at distance greater than i in G for every i, 1 ≤ i ≤ k. For a given integer p ≥ 1, the p-corona of a graph G is the graph obtained from G by adding p degree-one neighbors to every vertex of G. In this paper, we determine the packing chromatic number of p-coronae of paths and cycles for every p ≥ 1. Moreover, by considering digraphs and the (weak) directed distance between vertices, we get a natural extension of the notion of packing coloring to digraphs. We then determine the packing chromatic number of orientations of p-coronae of paths and cycles.
Keywords: packing coloring, packing chromatic number, corona graph, path, cycle 
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Laïche, Daouya; Bouchemakh, Isma; Sopena, Éric. Packing Coloring of Some Undirected and Oriented Coronae Graphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 665-690. http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a12/