The Sombor index of trees and unicyclic graphs with given matching number

In 2021, the Sombor index was introduced by Gutman, which is a new degree-based topological molecular descriptors. The Sombor index of a graph $G$ is defined as $SO(G)={\sum }_{uv\in E(G)}\sqrt{d_G^2(u)+d_G^2(v)}$, where $d_G(v)$ is the degree of the vertex $v$ in $G$. Let ${\mathcal{T}}_{n,m}$ and ${\mathcal{U}}_{n,m}$ be the set of trees and unicyclic graphs on $n$ vertices with fixed matching number $m$, respectively. In this paper, the tree and the unicyclic graph with the maximum Sombor index are determined among ${\mathcal{T}}_{n,m}$ and ${\mathcal{U}}_{n,m}$, respectively.