# Packing Coloring of Some Undirected and Oriented Coronae Graphs

Daouya Laïche; Isma Bouchemakh; Éric Sopena

Discussiones Mathematicae Graph Theory (2017)

- Volume: 37, Issue: 3, page 665-690
- ISSN: 2083-5892

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topDaouya Laïche, Isma Bouchemakh, and Éric Sopena. "Packing Coloring of Some Undirected and Oriented Coronae Graphs." Discussiones Mathematicae Graph Theory 37.3 (2017): 665-690. <http://eudml.org/doc/288517>.

@article{DaouyaLaïche2017,

abstract = {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.},

author = {Daouya Laïche, Isma Bouchemakh, Éric Sopena},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {packing coloring; packing chromatic number; corona graph; path; cycle},

language = {eng},

number = {3},

pages = {665-690},

title = {Packing Coloring of Some Undirected and Oriented Coronae Graphs},

url = {http://eudml.org/doc/288517},

volume = {37},

year = {2017},

}

TY - JOUR

AU - Daouya Laïche

AU - Isma Bouchemakh

AU - Éric Sopena

TI - Packing Coloring of Some Undirected and Oriented Coronae Graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2017

VL - 37

IS - 3

SP - 665

EP - 690

AB - 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.

LA - eng

KW - packing coloring; packing chromatic number; corona graph; path; cycle

UR - http://eudml.org/doc/288517

ER -

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