On the Difference of Atom-Bond Sum-Connectivity and Atom-Bond-Connectivity Indices

The atom-bond connectivity (ABC) index is one of the well-investigated degree-based topological indices. The atom-bond sum-connectivity (ABS) index is a modified version of the ABC index, which was introduced recently. The primary goal of the present paper is to investigate the difference between the aforementioned two indices, namely ABS - ABC. It is shown that the difference ABS - ABC is positive for all graphs of minimum degree at least 2 as well as for all line graphs of those graphs of order at least 5 that are different from the path and cycle graphs. By means of computer search, the difference ABS - ABC is also calculated for all trees of order at most 15.