  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, is adjacent to (i - 1) vertices colored with each color
j, 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
