Proof of an open problem on the Sombor index

The Sombor index is one of the geometry-based descriptors, which was defined as $$\begin{aligned} SO(G)=\sum _{uv\in E(G)}\sqrt{d^{2}_{u}+d^{2}_{v}}, \end{aligned}$$ where $$d_{u}$$ (resp. $$d_{v}$$ ) denotes degree vertex u v) in G. In this note, we determine graphs among set with connectivity edge connectivity) at most k having maximum and minimum indices, solves an open problem on proposed by Hayat Rehman [On a given number cut-vertices, MATCH Commun. Math. Comput. Chem. 89 (2023) 437–450]. For some conclusions above paper, first give counterexamples, then provide another simple proof about indices n vertices, cut vertices least cycle.