Greedy trees have minimum Sombor indices

Recently, Gutman [MATCH Commun. Math. Comput. Chem. 86 (2021) 11-16] defined a new graph invariant which is named the Sombor index $\mathrm{S}\mathrm{O}(G)$ of a graph $G$ and is computed via the expression $$\mathrm{S}\mathrm{O}(G)=\sum _{u\sim v}\sqrt{\mathrm{d}\mathrm{e}\mathrm{g}(u{)}^2+\mathrm{d}\mathrm{e}\mathrm{g}(v{)}^2},$$ where $\mathrm{d}\mathrm{e}\mathrm{g}(u)$ represents the degree of the vertex $u$ in $G$ and the summing is performed across all the unordered pairs of adjacent vertices $u$ and $v$. Here we take into consideration the set of all the trees ${\mathcal{T}}_D$ that have a specified degree sequence $D$ and show that the greedy tree attains the minimum Sombor index on the set ${\mathcal{T}}_D$.