University of IsfahanTransactions on Combinatorics2251-86572220130601Modular chromatic number of $C_m square P_n$4772294310.22108/toc.2013.2943ENN.ParamaguruAnnamalai UniversityR.SampathkumarAnnamalai UniversityJournal Article20130125A modular $k!$-coloring, $kge 2,$ 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 $C_msquare P_n$ is determined.https://toc.ui.ac.ir/article_2943_5fa15d9e433e3cf4e5d1849c0214c4df.pdf