Abstract
Circulant graphs are characterized here as quotient lattices, which are realized as vertices connected by a knot on a k -dimensional flat torus tessellated by hypercubes or hyperparallelotopes. Via this approach we present geometric interpretations for a bound on the diameter of a circulant graph, derive new bounds for the genus of a class of circulant graphs and establish connections with spherical codes and perfect codes in Lee spaces.
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