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Mathematical Properties of the Hyperbolicity of Circulant Networks

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  • Juan C. Hernández
  • José M. Rodríguez
  • José M. Sigarreta

Abstract

If is a geodesic metric space and , a geodesic triangle    is the union of the three geodesics , , and in . The space is - hyperbolic (in the Gromov sense) if any side of is contained in a -neighborhood of the union of the two other sides, for every geodesic triangle in . The study of the hyperbolicity constant in networks is usually a very difficult task; therefore, it is interesting to find bounds for particular classes of graphs. A network is circulant if it has a cyclic group of automorphisms that includes an automorphism taking any vertex to any other vertex. In this paper we obtain several sharp inequalities for the hyperbolicity constant of circulant networks; in some cases we characterize the graphs for which the equality is attained.

Suggested Citation

  • Juan C. Hernández & José M. Rodríguez & José M. Sigarreta, 2015. "Mathematical Properties of the Hyperbolicity of Circulant Networks," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-11, November.
    • Handle: RePEc:hin:jnlamp:723451
    DOI: 10.1155/2015/723451
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