Abstract: Let $G$ be a simple connected graph with vertex set $V(G)$ and edge set $E(G)$. Then the Sombor index of graph $G$ is defined as $SO(G)=\sum_{uv\in E(G)}\sqrt{d^2(u)+d^2(v)}$, where $d(u)$ denotes the degree of vertex $u$. In this paper, the maximum and minimum values of the Sombor index for Halin graphs are obtained, and the corresponding extremal graphs are characterized.

Key words: Halin graph, Sombor index, Extreme value