Abstract
Ali et al. [3] introduced a new type of vertex-degree-based topological indices of a graph which is called as atom-bond sum-connectivity (ABS) index. For a graph \( G=(V(G),E(G)) \), the ABS index of \( G \) 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 \( G \). Recall that \( G \) is a molecular graph if \( d_G(u)\leq 4 \) for all \( u \in V(G) \). In this paper, we characterize molecular trees with a perfect matching
attaining the maximum ABS index.
