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 ABSโABC. It is shown that the difference
ABSโABC 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
ABSโABC is also calculated for all trees of order at most 15.Comment: 16 pages and 5 figure