Grundy number of graphs | Zendy

Brice Effantin | Zendy; Hamamache Kheddouci | Zendy

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Grundy number of graphs

Author(s) -

Brice Effantin,

Hamamache Kheddouci

Publication year - 2007

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1339

Subject(s) - combinatorics , mathematics , colored , vertex (graph theory) , cartesian product , graph , polygon mesh , discrete mathematics , geometry , materials science , composite material

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.

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