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 K1,4 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 (2δ−1)2 (where δ is the minimum degree and δ≥2)
and for some families of trees. Thereby, a partial solution to an open problem
proposed by Das and Trinajsti\'{c} is given.Comment: 10 pages, 2 tables, 1 figure, revised versio