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On the geometric–arithmetic index by decompositions-CMMSE

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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. There are many papers studying different kinds of indices (as Wiener, hyper–Wiener, detour, hyper–detour, Szeged, edge–Szeged, PI, vertex–PI and eccentric connectivity indices) under particular cases of decompositions. The main aim of this paper is to show that the computation of the geometric-arithmetic index of a graph G is essentially reduced to the computation of the geometric-arithmetic indices of the so-called primary subgraphs obtained by a general decomposition of G. Furthermore, using these results, we obtain formulas for the geometric-arithmetic indices of bridge graphs and other classes of graphs, like bouquet of graphs and circle graphs. These results are applied to the computation of the geometric-arithmetic index of Spiro chain of hexagons, polyphenylenes and polyethene.

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Authors and Affiliations

  1. Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No. 54 Col. Garita, 39650, Acalpulco Gro, Mexico

    Juan C. Hernández & José M. Sigarreta

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

    José M. Rodríguez

Authors
  1. Juan C. Hernández
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  2. José M. Rodríguez
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  3. José M. Sigarreta
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Corresponding author

Correspondence to José M. Rodríguez.

Additional information

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

Juan C. Hernández, José M. Rodríguez, José M. Sigarreta: Supported in part by a grant from CONACYT (FOMIX-CONACyT-UAGro 249818), México. José M. Rodríguez, José M. Sigarreta: Supported in part by two grants from Ministerio de Economía y Competitividad (MTM 2013-46374-P and MTM 2015-69323-REDT), Spain.

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Hernández, J.C., Rodríguez, J.M. & Sigarreta, J.M. On the geometric–arithmetic index by decompositions-CMMSE. J Math Chem 55, 1376–1391 (2017). https://doi.org/10.1007/s10910-016-0681-0

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  • DOI: https://doi.org/10.1007/s10910-016-0681-0

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