%0 Journal Article
%T Modular chromatic number of $C_m square P_n$
%J Transactions on Combinatorics
%I University of Isfahan
%Z 2251-8657
%A Paramaguru, N.
%A Sampathkumar, R.
%D 2013
%\ 06/01/2013
%V 2
%N 2
%P 47-72
%! Modular chromatic number of $C_m square P_n$
%K modular coloring
%K modular chromatic number
%K Cartesian product
%R 10.22108/toc.2013.2943
%X A 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.
%U https://toc.ui.ac.ir/article_2943_5fa15d9e433e3cf4e5d1849c0214c4df.pdf