The GridGraph(m,n) command creates the m by n grid graph on m*n vertices.

The TorusGridGraph(m,n) creates the m by n torus grid graph on m*n vertices.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$$\mathrm{with}\left(\mathrm{SpecialGraphs}\right)\:$

$G≔\mathrm{GridGraph}\left(5\,3\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 15\; vertices\; and\; 22\; edges}$

$\mathrm{IsBipartite}\left(G\right)$

$\mathrm{true}$

$\mathrm{DrawGraph}\left(G\right)$

$H≔\mathrm{TorusGridGraph}\left(5\,3\right)\:$

$\mathrm{IsBipartite}\left(H\right)$

$\mathrm{false}$

$\mathrm{DrawGraph}\left(H\right)$