Modular chromatic number of $C_m square P_n$

Abstract

A modular $k$-coloring, $kge 2,$ of a graph $G$ without isolated vertices 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 the 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 $C_msquare P_n$ is determined.

Keywords

• modular coloring
• modular chromatic number
• Cartesian product