Abstract
Introduced by Gutman in 2021, the Sombor index is a novel graph-theoretic topological descriptor possessing potential applications in the modeling of thermodynamic properties of compounds. Let \(\mathbb{H}_n^k\) be the family of graphs on order \(n\)
and \(k\) number of cut-vertices having at least one cycle. In this paper, we present minimum Sombor indices of graphs in \(\mathbb{H}_n^k\). The corresponding extremal graphs have been characterized as well.
