Torus graph
= Torus graph
{title2=$\mathbb T_N=C_N\mathbin\square C_N$}
For $N\geq3$, the square torus graph has vertex set $(\mathbb Z/N\mathbb Z)^2$ and joins vertices differing by one in exactly one coordinate. It has $N^2$ vertices and $2N^2$ bonds. Translations act transitively on vertices; translations together with a quarter turn act transitively on bonds. A rectangle of side lengths at most $N-2$ has the same induced subgraph as its planar <square lattice> counterpart.