Journal of Mathematical Chemistry

, Volume 55, Issue 7, pp 1376–1391 | Cite as

On the geometric–arithmetic index by decompositions-CMMSE

  • Juan C. Hernández
  • José M. Rodríguez
  • José M. Sigarreta
Original Paper


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.


Graph invariant Topological index Geometric–arithmetic index 

Mathematics Subject Classification

05C07 92E10 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Juan C. Hernández
    • 1
  • José M. Rodríguez
    • 2
  • José M. Sigarreta
    • 1
  1. 1.Facultad de MatemáticasUniversidad Autónoma de GuerreroAcalpulco GroMexico
  2. 2.Departamento de MatemáticasUniversidad Carlos III de MadridLeganés, MadridSpain

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