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arXiv · 1401.7514

More on Comparison Between First Geometric-Arithmetic Index and Atom-Bond Connectivity Index

Zahid Raza·Akhlaq Ahmad Bhatti·Akbar Ali
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Abstract

The first geometric-arithmetic (GA) index and atom-bond connectivity (ABC) index are molecular structure descriptors which play a significant role in quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies. Das and Trinajsti\'{c} [\textit{Chem. Phys. Lett.} \textbf{497} (2010) 149-151] showed that $GA$ index is greater than $ABC$ index for all those graphs (except $K_{1,4}$ and $T^{*}$, see Figure 1) in which the difference between maximum and minimum degree is less than or equal to 3. In this note, it is proved that $GA$ index is greater than $ABC$ index for line graphs of molecular graphs, for general graphs in which the difference between maximum and minimum degree is less than or equal to $(2\delta-1)^{2}$ (where $\delta$ is the minimum degree and $\delta\geq2$) and for some families of trees. Thereby, a partial solution to an open problem proposed by Das and Trinajsti\'{c} is given.

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Zahid Raza, Akhlaq Ahmad Bhatti, Akbar Ali. 2014-01-29. More on Comparison Between First Geometric-Arithmetic Index and Atom-Bond Connectivity Index. https://doi.org/10.18514/mmn.2016.1265

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