Recently, the atom-bond sum-connectivity index (denoted as \( ABS \)) was introduced as a novel topological index in chemical graph theory. The \( ABS \) index of a graph \( G \) is defined as \[ ABS(G) = \sum_{v_i v_j \in E(G)} \sqrt{\frac{d_i + d_j - 2}{d_i + d_j}}\,, \] where \( d_i \) represents the degree of the vertex \( v_i \) in \( G \). An important problem in discrete mathematics is the characterization of extremal structures concerning graph invariants within the class of bicyclic graphs. In this context, Ali et al. [Extremal results and bounds for the atom-bond sum-connectivity index, MATCH Commun. Math. Comput. Chem. 92 (2024) 271-314] proposed a conjecture regarding the characterization of bicyclic graphs that minimize the \( ABS \) index.

This article fully characterizes the bicyclic graph that achieves the minimum \( ABS \) index, thereby resolving the conjecture.