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, 1-11

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.

Date: 2015
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AMP/2015/723451.pdf (application/pdf)
http://downloads.hindawi.com/journals/AMP/2015/723451.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:723451

DOI: 10.1155/2015/723451

Access Statistics for this article

More articles in Advances in Mathematical Physics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().