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 Trinajstic [Chem. Phys. Lett. 497 (2010) 149-151] showed that GA index is greater than ABC index for all those graphs (except K-1,K- 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 >= 2) and for some families of trees. Therefore, a partial solution to an open problem proposed by Das and Trinajstic is given.