Circulant graphs and tessellations on flat tori

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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. © 2010 Elsevier Inc. All rights reserved.

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Costa, S. I. R., Strapasson, J. E., Alves, M. M. S., & Carlos, T. B. (2011). Circulant graphs and tessellations on flat tori. Linear Algebra and Its Applications, 434(8), 1811–1823. https://doi.org/10.1016/j.laa.2009.08.019

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