The Grundy number of a graph G is the maximum number k of colors used to color the vertices of G such that the coloring is proper and every vertex x colored with color i, 1 ≤ i ≤ k, is adjacent to (i-1) vertices colored with each color j, 1 ≤ j ≤ i -1. In this paper we give bounds for the Grundy number of some graphs and cartesian products of graphs. In particular, we determine an exact value of this parameter for n-dimensional meshes and some n-dimensional toroidal meshes. Finally, we present an algorithm to generate all graphs for a given Grundy number.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1339,
author = {Brice Effantin and Hamamache Kheddouci},
title = {Grundy number of graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {27},
year = {2007},
pages = {5-18},
zbl = {1133.05031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1339}
}
Brice Effantin; Hamamache Kheddouci. Grundy number of graphs. Discussiones Mathematicae Graph Theory, Tome 27 (2007) pp. 5-18. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1339/
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