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CMMSE: A new approximation to the geometric–arithmetic index

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Abstract

The concept of geometric–arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new inequalities involving the geometric–arithmetic index \(GA_1\) and characterize graphs extremal with respect to them.

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References

  1. K.C. Das, On geometric–arithmetic index of graphs. MATCH Commun. Math. Comput. Chem. 64, 619–630 (2010)

    Google Scholar 

  2. K.C. Das, I. Gutman, B. Furtula, Survey on geometric–arithmetic indices of graphs. MATCH Commun. Math. Comput. Chem. 65, 595–644 (2011)

    CAS  Google Scholar 

  3. K.C. Das, I. Gutman, B. Furtula, On first geometric-arithmetic index of graphs. Discrete Appl. Math. 159, 2030–2037 (2011)

    Article  Google Scholar 

  4. B. Furtula, I. Gutman, A forgotten topological index. J. Math. Chem. 53(4), 1184–1190 (2015)

    Article  CAS  Google Scholar 

  5. I. Gutman, B. Furtula (eds.), Recent Results in the Theory of Randić Index (Univ. Kragujevac, Kragujevac, 2008)

    Google Scholar 

  6. X. Li, I. Gutman, Mathematical Aspects of Randić Type Molecular Structure Descriptors (Univ. Kragujevac, Kragujevac, 2006)

    Google Scholar 

  7. X. Li, Y. Shi, A survey on the Randić index. MATCH Commun. Math. Comput. Chem. 59, 127–156 (2008)

    CAS  Google Scholar 

  8. A. Miličević, S. Nikolić, On variable Zagreb indices. Croat. Chem. Acta 77, 97–101 (2004)

    Google Scholar 

  9. M. Mogharrab, G.H. Fath-Tabar, Some bounds on \(GA_1\) index of graphs. MATCH Commun. Math. Comput. Chem. 65, 33–38 (2010)

    Google Scholar 

  10. C. P. Niculescu, Converses of the Cauchy-Schwarz inequality in the \(C^*\)-framework. https://www.researchgate.net/publication/252235293_Converses_of_the_Cauchy-Schwarz_inequality_in_the_C-framework

  11. S. Nikolić, G. Kovačević, A. Miličević, N. Trinajstić, The Zagreb Indices 30 years after. Croat. Chem. Acta 76, 113–124 (2003)

    Google Scholar 

  12. M. Randić, On characterization of molecular branching. J. Am. Chem. Soc. 97, 6609–6615 (1975)

    Article  Google Scholar 

  13. J.M. Rodríguez, J.M. Sigarreta, On the geometric–arithmetic index. MATCH Commun. Math. Comput. Chem. 74, 103–120 (2015)

    Google Scholar 

  14. J.M. Rodríguez, J.M. Sigarreta, Spectral properties of geometric–arithmetic index. Appl. Math. Comput. 277, 142–153 (2016)

    Google Scholar 

  15. J.A. Rodríguez-Velázquez, J.M. Sigarreta, On the Randić index and condicional parameters of a graph. MATCH Commun. Math. Comput. Chem. 54, 403–416 (2005)

    Google Scholar 

  16. J.A. Rodríguez-Velázquez, J. Tomás-Andreu, On the Randić index of polymeric networks modelled by generalized Sierpinski graphs. MATCH Commun. Math. Comput. Chem. 74, 145–160 (2015)

    Google Scholar 

  17. J.M. Sigarreta, Bounds for the geometric–arithmetic index of a graph. Miskolc Math. Notes 16, 1199–1212 (2015)

    Article  Google Scholar 

  18. TRC Thermodynamic Tables. Hydrocarbons; Thermodynamic Research Center, The Texas A & M University System: College Station, TX (1987)

  19. M. Vöge, A.J. Guttmann, I. Jensen, On the number of benzenoid hydrocarbons. J. Chem. Inf. Comput. Sci. 42, 456–466 (2002)

    Article  CAS  PubMed  Google Scholar 

  20. D. Vukičević, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges. J. Math. Chem. 46, 1369–1376 (2009)

    Article  CAS  Google Scholar 

  21. G.S. Watson, Serial correlation in regression analysis I. Biometrika 42, 327–342 (1955)

    Article  Google Scholar 

  22. H. Wiener, Structural determination of paraffin boiling points. J. Am. Chem. Soc. 69, 17–20 (1947)

    Article  CAS  PubMed  Google Scholar 

  23. B. Zhou, N. Trinajstić, On general sum-connectivity index. J. Math. Chem. 47, 210–218 (2010)

    Article  CAS  Google Scholar 

Download references

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Authors and Affiliations

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

    Alvaro Martínez-Pérez

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

    José M. Rodríguez

  3. Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame 5, Col. La Garita, Acapulco, Gro, Mexico

    José M. Sigarreta

Authors
  1. Alvaro Martínez-Pérez
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  2. José M. Rodríguez
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  3. José M. Sigarreta
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Corresponding author

Correspondence to Alvaro Martínez-Pérez.

Additional information

This is one of several papers published together in Journal of Mathematical Chemistry on the “Special Issue: CMMSE 2017”.

First author supported in part by a grant from Ministerio de Economía y Competitividad (MTM 2015-63612P), Spain. Second and third authors supported in part by two grants from Ministerio de Economía y Competitividad (MTM 2016-78227-C2-1-P and MTM 2015-69323-REDT), Spain, and a grant from CONACYT (FOMIX-CONACyT-UAGro 249818), México.

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Martínez-Pérez, A., Rodríguez, J.M. & Sigarreta, J.M. CMMSE: A new approximation to the geometric–arithmetic index. J Math Chem 56, 1865–1883 (2018). https://doi.org/10.1007/s10910-017-0811-3

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  • DOI: https://doi.org/10.1007/s10910-017-0811-3

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