General approach for obtaining extremal results on degree-based indices illustrated on the general sum-connectivity index - Tomáš Vetrík (Electronic Journal of Graph Theory and Applications (EJGTA), 2023)
Among bipartite graphs with given order and matching number/vertex cover number/edge cover number/independence number, among multipartite graphs with given order, and among graphs with given order and chromatic number, we present the graphs having the maximum degree-based index if that index satisfies certain conditions. We show that those conditions are satisfied by the general sum-connectivity index χa for all or some a ≥ 0.