Circulant graphs and tessellations on flat tori |
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| Authors: | S.I.R. Costa J.E. Strapasson M.M.S. Alves |
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| Affiliation: | a Institute of Mathematics, State University of Campinas, UNICAMP, CEP 13081-970, Campinas, SP, Brazil
b Department of Mathematics, Federal University of Paraná, CEP 81531-990, Curitiba, Brazil |
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| 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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| Keywords: | 05C50 05E20 52C07 05C10 |
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