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The hyperbolicity constant of infinite circulant graphs

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.contributor.authorRodríguez García, José Manuel
dc.contributor.authorSigarreta Almira, José María
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2023-10-06T12:41:05Z
dc.date.available2023-10-06T12:41:05Z
dc.date.issued2017-06-09
dc.description.abstractIf 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.en
dc.description.sponsorshipThe 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.en
dc.format.extent15es
dc.identifier.bibliographicCitationRodrı́guez, J. M., & Sigarreta, J. M. (2017). The hyperbolicity constant of infinite circulant graphs. Open Mathematics, vol. 15, no. 1, 2017, pp. 800-814en
dc.identifier.doihttps://doi.org/10.1515/math-2017-0061
dc.identifier.issn2391-5455
dc.identifier.publicationfirstpage800es
dc.identifier.publicationissue1es
dc.identifier.publicationlastpage814es
dc.identifier.publicationtitleOpen Mathematicsen
dc.identifier.publicationvolume15es
dc.identifier.urihttps://hdl.handle.net/10016/38572
dc.identifier.uxxiAR/0000020276
dc.language.isoengen
dc.publisherWalter de Gruyter GmbHen
dc.relation.projectIDGobierno de España. MTM2013-46374-Pes
dc.relation.projectIDGobierno de España. MTM2015-69323-REDTes
dc.rights© 2017 Rodríguez and Sigarreta. Published by De Gruyter Open Accessen
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subject.ecienciaMatemáticases
dc.subject.otherGeodesicsen
dc.subject.otherCirculant graphen
dc.subject.otherGromov hyperbolicityen
dc.subject.otherInfinite graphsen
dc.titleThe hyperbolicity constant of infinite circulant graphsen
dc.typeresearch article*
dc.type.hasVersionVoR*
dspace.entity.typePublication
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