Recently, Ali et al. [1] posed several open problems concerning extremal graphs with respect to the atom-bond sum connectivity index. These problems involve characterizing graphs that attain the maximum \( ABS \) index within specific graph classes, including: (i) connected graphs with \( n \) vertices and \( p \) cut-vertices; (ii) connected graphs of order \( n \) with vertex \( k \)-partiteness \( v_k(G) = r \); and (iii) connected bipartite graphs of order \( n \) with a fixed vertex connectivity \( \kappa \). In this paper, we provide complete solutions to all of these problems.