Hyperbolicity of direct products of graphs

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dc.contributor.author Carballosa Torres, Walter
dc.contributor.author Cruz Rodríguez, Amauris de la
dc.contributor.author Martinez Perez, Alvaro
dc.contributor.author Rodríguez García, José Manuel
dc.date.accessioned 2019-02-11T08:43:26Z
dc.date.available 2019-02-11T08:43:26Z
dc.date.issued 2018-07-12
dc.identifier.bibliographicCitation Carballosa, W., de la Cruz, A., Martínez-Pérez, A., Rodríguez, J.M. (2018). Hyperbolicity of Direct Products of Graphs. Symmetry, 10 (7), 279.
dc.identifier.issn 2073-8994
dc.identifier.uri http://hdl.handle.net/10016/28036
dc.description.abstract It is well-known that the different products of graphs are some of the more symmetric classes of graphs. Since we are interested in hyperbolicity, it is interesting to study this property in products of graphs. Some previous works characterize the hyperbolicity of several types of product graphs (Cartesian, strong, join, corona and lexicographic products). However, the problem with the direct product is more complicated. The symmetry of this product allows us to prove that, if the direct product G(1) x G(2) is hyperbolic, then one factor is bounded and the other one is hyperbolic. Besides, we prove that this necessary condition is also sufficient in many cases. In other cases, we find (not so simple) characterizations of hyperbolic direct products. Furthermore, we obtain good bounds, and even formulas in many cases, for the hyperbolicity constant of the direct product of some important graphs (as products of path, cycle and even general bipartite graphs).
dc.description.sponsorship This work was supported in part by four grants from Ministerio de Economía y Competititvidad (MTM2012-30719, MTM2013-46374-P, MTM2016-78227-C2-1-P and MTM2015-69323-REDT), Spain.
dc.format.extent 27
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher MDPI
dc.rights © 2018 by the authors; licensee MDPI, Basel, Switzerland.
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other Direct product of graphs
dc.subject.other Geodesics
dc.subject.other Gromov hyperbolicity
dc.subject.other Bipartite graphs
dc.title Hyperbolicity of direct products of graphs
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.3390/sym10070279
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2012-30719
dc.relation.projectID Gobierno de España. MTM2013-46374-P
dc.relation.projectID Gobierno de España. MTM2016-78227-C2-1-P
dc.relation.projectID Gobierno de España. MTM2015-69323-REDT
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 1
dc.identifier.publicationissue 7
dc.identifier.publicationlastpage 25
dc.identifier.publicationtitle Symmetry-Basel
dc.identifier.publicationvolume 10 (279)
dc.identifier.uxxi AR/0000021901
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