Abstract
The atom-bond sum-connectivity (ABS) index of a graph \( G \), introduced by Ali et al., is defined as
\[
ABS(G)=\sum_{uv\in E(G)}\sqrt{1\!-\!\frac{2}{d_G(u)\!+\!d_G(v)}},
\]
where \( d_G(u) \) denotes the degree of the vertex \( u \) in \( G \).
In this paper, we present the extremal trees with the maximum ABS index among all trees of a given order with matching
number or diameter, respectively. Moreover, the tree with a perfect matching having the maximum ABS index is also
determined.
