Toroidal graph

A toroidal graph that cannot be embedded in a plane is said to have genus 1.

[5] By a result analogous to Fáry's theorem, any toroidal graph may be drawn with straight edges in a rectangle with periodic boundary conditions.

[6] Furthermore, the analogue of Tutte's spring theorem applies in this case.

[7] Toroidal graphs also have book embeddings with at most 7 pages.

Alternatively, there are at least 250,815 non-toroidal graphs that are minimal in the topological minor ordering.