Mathematical Properties of the Hyperbolicity of Circulant Networks

Juan C. Hernández, José M. Rodríguez and José M. Sigarreta

Advances in Mathematical Physics, 2015, vol. 2015, issue 1

Abstract: If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3], and [x3x1] in X. The space X is δ‐hyperbolic (in the Gromov sense) if any side of T is contained in a δ‐neighborhood of the union of the two other sides, for every geodesic triangle T in X. 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.

Date: 2015
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https://doi.org/10.1155/2015/723451

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:723451

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