MMN-1265
More on comparison between first geometric-arithmetic index and atom-bond connectivity index
Zahid Raza; Akhlaq Ahmad Bhatti; Akbar Ali;Abstract
The recently introduced first geometric-arithmetic (GA) index and atom-bond connectivity (ABC) index are molecular structure descriptors which play a significant role in QSPR/QSAR studies. K. C. Das and N. Trinajsti$\acute{c}$ [\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 three. In this note, we prove 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 ($\delta>1$) is less than or equal to $(2\delta-1)^{2}$ and for some families of trees; giving partial solution to an open problem proposed by K. C. Das and N. Trinajsti$\acute{c}$.
Vol. 17 (2016), No. 1, pp. 561-570
DOI: 10.18514/MMN.2016.1265