Abstract
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.
