More on comparison between first geometric-arithmetic index and atom-bond connectivity index

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 Trinajstić [Chem. Phys. Lett. 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. Therefore, a partial solution to an open problem proposed by Das and Trinajstić is given.