RT Journal Article
T1 The hyperbolicity constant of infinite circulant graphs
A1 Rodríguez García, José Manuel
A1 Sigarreta Almira, José María
AB If X is a geodesic metric space and x(1), x(2), x(3) is an element of X, a geodesic triangle T = {x(1), x(2), x(3)} is the union of the three geodesics [x(1)x(2)], [x(2)x(3)] and [x(3)x(1)] in X. The space X is delta-hyperbolic (in the Gromov sense) if any side of T is contained in a delta-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.
PB Walter de Gruyter GmbH
SN 2391-5455
YR 2017
FD 2017-06-09
LK https://hdl.handle.net/10016/38572
UL https://hdl.handle.net/10016/38572
LA eng
NO The authors thank the referees for their deep revision of the manuscript. Their comments and suggestions have contributed to improve substantially the presentation of this work. This work is supported in part by two grants from Ministerio de Economía y Competititvidad (MTM2013-46374-P and MTM2015-69323-REDT), Spain, and a grant from CONACYT (FOMIX-CONACyT-UAGro 249818), México. The first author is supported in part by two grants from Ministerio de Economía y Competititvidad (MTM2013- 46374-P and MTM2015-69323-REDT), Spain, and a grant from CONACYT (FOMIX-CONACyT-UAGro 249818), México.
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RD 17 jul. 2024