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Some results on lower bounds for topological indices

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Abstract

The aim of this paper is to obtain new inequalities involving some topological indices of a graph and characterize graphs extremal with respect to them. Our main results provide lower bounds on several indices involving just the minimum and the maximum degree of the graph G. This family of indices includes, among others, the Wiener index and several of its generalizations, the harmonic index and the general sum-connectivity index, and the geometric-arithmetic index. We also include some chemical applications of our results and some open problems.

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Authors and Affiliations

  1. Facultad CC. Sociales de Talavera, Avda. Real Fábrica de Seda, s/n., 45600, Talavera de la Reina, Toledo, Spain

    Álvaro Martínez-Pérez

  2. Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911, Leganés, Madrid, Spain

    José M. Rodríguez

Authors
  1. Álvaro Martínez-Pérez
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  2. José M. Rodríguez
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Correspondence to Álvaro Martínez-Pérez.

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Álvaro Martínez-Pérez was supported in part by a Grant from Ministerio de Economía y Competitividad (MTM 2015-63612P), Spain. José M. Rodríguez 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 MTM2015-69323-REDT), Spain.

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Martínez-Pérez, Á., Rodríguez, J.M. Some results on lower bounds for topological indices. J Math Chem 57, 1472–1495 (2019). https://doi.org/10.1007/s10910-018-00999-7

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  • DOI: https://doi.org/10.1007/s10910-018-00999-7

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