# Modular chromatic number of $C_m \square P_n$

Document Type: Research Paper

Authors

Annamalai University

Abstract

A modular $k\!$-coloring‎, ‎$k\ge 2,$ 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.

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### References

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