Circulant Graphs Viewed as Graphs on Flat Tori

Circulant graphs can be viewed as vertices connected by a knot on a $k$-dimensional flat torus tessellated by hypercubes or hyperparallelotopes. This approach allows to see some results on circulant graph minimum diameter, to derive bounds for the genus of certain circulant graphs and also to establish connections with spherical codes and perfect graph codes in Lee spaces.