The hyperbolicity constant of infinite circulant graphs

• Autorzy: José M. Rodríguez , José M. Sigarreta
• Języki publikacji: EN

Abstrakty

EN

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. Deciding whether or not a graph is hyperbolic is usually very difficult; therefore, it is interesting to find classes of graphs which are hyperbolic. A graph 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 prove that infinite circulant graphs and their complements are hyperbolic. Furthermore, we obtain several sharp inequalities for the hyperbolicity constant of a large class of infinite circulant graphs and the precise value of the hyperbolicity constant of many circulant graphs. Besides, we give sharp bounds for the hyperbolicity constant of the complement of every infinite circulant graph.

Słowa kluczowe

EN

Circulant graph; Gromov hyperbolicity; Geodesics; Infinite graphs

Kategorie tematyczne

• 05C12: Distance in graphs
• 05A20: Combinatorial inequalities
• 05C75: Structural characterization of families of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 800-814

Daty

wydano

2017-01-01

otrzymano

2016-06-21

zaakceptowano

2017-03-30

online

2017-06-09

Twórcy

autor

José M. Rodríguez

• , , , ,

autor

José M. Sigarreta

• , , .,

Identyfikatory

DOI

10.1515/math-2017-0061