# Grundy number of graphs

• Volume: 27, Issue: 1, page 5-18
• ISSN: 2083-5892

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## Abstract

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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.

## How to cite

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Brice Effantin, and Hamamache Kheddouci. "Grundy number of graphs." Discussiones Mathematicae Graph Theory 27.1 (2007): 5-18. <http://eudml.org/doc/270336>.

@article{BriceEffantin2007,
abstract = {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.},
author = {Brice Effantin, Hamamache Kheddouci},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {Grundy coloring; vertex coloring; cartesian product; graph product; meshes; algorithm},
language = {eng},
number = {1},
pages = {5-18},
title = {Grundy number of graphs},
url = {http://eudml.org/doc/270336},
volume = {27},
year = {2007},
}

TY - JOUR
AU - Brice Effantin
AU - Hamamache Kheddouci
TI - Grundy number of graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2007
VL - 27
IS - 1
SP - 5
EP - 18
AB - 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.
LA - eng
KW - Grundy coloring; vertex coloring; cartesian product; graph product; meshes; algorithm
UR - http://eudml.org/doc/270336
ER -

## References

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