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Computational and analytical studies of the Randic index in Erdös-Rényi models

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorMartínez-Martínez, C. T.
dc.contributor.authorMéndez-Bermúdez, J. A.
dc.contributor.authorRodríguez García, José Manuel
dc.contributor.authorSigarreta Almira, José María
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.contributor.funderAgencia Estatal de Investigación (España)es
dc.date.accessioned2023-09-11T08:25:53Z
dc.date.available2023-09-11T08:25:53Z
dc.date.issued2020-07-15
dc.description.abstractIn this work we perform computational and analytical studies of the Randic´ index R(G) in Erdös–Rényi models G(n, p) characterized by n vertices connected independently with probability p ∈ (0, 1). First, from a detailed scaling analysis, we show that R(G) = {R(G)}/(n/2) scales with the product ξ ≈ np, so we can define three regimes: a regime of mostly isolated vertices when ξ < 0.01 (R(G) ≈ 0), a transition regime for 0.01 < ξ < 10 (where 0 < R(G) < n/2), and a regime of almost complete graphs for ξ > 10 (R(G) ≈ n/2). Then, motivated by the scaling of R(G), we analytically (i) obtain new relations connecting R(G) with other topological indices and characterize graphs which are extremal with respect to the relations obtained and (ii) apply these results in order to obtain inequalities on R(G) for graphs in Erdös–Rényi models.en
dc.description.sponsorshipJ.A.M.-B. acknowledges financial support from FAPESP (Grant No. 2019/06931-2), Brazil, and PRODEP-SEP (Grant No. 511- 6/2019.-11821), Mexico. J.M.R. and J.M.S. were supported in part by two grants from Ministerio de Economía y Competitividad, Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) (MTM2016-78227-C2-1-P and MTM2017-90584-REDT), Spain.en
dc.format.extent14
dc.identifier.bibliographicCitationMartinez-Martinez, C. T., Méndez-Bermúdez, J. A., Rodríguez, J. M., & Sigarreta, J. M. (2020). Computational and analytical studies of the Randić Index in Erdös–Rényi models. Applied Mathematics and Computation, 377, 125137.en
dc.identifier.doihttps://doi.org/10.1016/j.amc.2020.125137
dc.identifier.issn0096-3003
dc.identifier.publicationfirstpage1
dc.identifier.publicationissue125137
dc.identifier.publicationlastpage14
dc.identifier.publicationtitleApplied Mathematics and Computationen
dc.identifier.publicationvolume377
dc.identifier.urihttps://hdl.handle.net/10016/38284
dc.identifier.uxxiAR/0000026810
dc.language.isoengen
dc.publisherElsevieren
dc.relation.projectIDGobierno de España. MTM2016-78227-C2-1-Pes
dc.relation.projectIDGobierno de España. MTM2017-90584-REDTes
dc.rights© 2020 Elsevier Inc.en
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.otherRandic indexen
dc.subject.otherVertex-degree-based topologicalen
dc.subject.otherIndex random graphsen
dc.subject.otherErdös-Rényi graphsen
dc.titleComputational and analytical studies of the Randic index in Erdös-Rényi modelsen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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