N. Paramaguru - Annamalai University
R. Sampathkumar - Annamalai University

A modular k\!-coloring‎, ‎k\ge ۲, of a graph G is a coloring of the vertices of G with the elements in \mathbb{Z}_k having the property that for every two adjacent vertices of G, the sums of the colors of their neighbors are different in \mathbb{Z}_k. The minimum k for which G has a modular k\!-coloring is the modular chromatic number of G. Except for some special cases‎, ‎modular chromatic number of C_m\square P_n is determined‎.

modular coloring, modular chromatic number, Cartesian product