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Relations between some topological indices and the line graph

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Abstract

The concepts of geometric–arithmetic and harmonic indices were introduced in the area of chemical graph theory recently. They have proven to correlate well with physical and chemical properties of some molecules. The aim of this paper is to obtain new inequalities involving the first Zagreb, the harmonic, and the geometric–arithmetic \(GA_1\) indices. Furthermore, inequalities relating these indices and line graphs are proven.

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Correspondence to Domingo Pestana.

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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.

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Carballosa, W., Granados, A., Pestana, D. et al. Relations between some topological indices and the line graph. J Math Chem 58, 632–646 (2020). https://doi.org/10.1007/s10910-019-01091-4

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Keywords

  • First Zagreb index
  • Geometric–arithmetic index
  • Harmonic index
  • Vertex–degree-based topological index
  • Line graph

Mathematics Subject Classification

  • MSC 05C07
  • MSC 92E10