  The atom-bond sum-connectivity (ABS) index of a graph $G$ with edges
$e_1,\cdots,e_m$ is the sum of the numbers $\sqrt{1-2(d_{e_i}+2)^{-1}}$ over
$1\le i \le m$, where $d_{e_i}$ is the number of edges adjacent with $e_i$. In
this paper, we study the maximum values of the ABS index over graphs with given
parameters. More specifically, we determine the maximum ABS index of connected
graphs of a given order and with a fixed (i) minimum degree, (ii) maximum
degree, (iii) chromatic number, (iv) independence number, or (v) number of
pendent vertices. We also characterize the graphs attaining the maximum ABS
values in all of these classes.
