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Recently, Gutman [MATCH Commun. Math. Comput. Chem. 86 (2021) 11-16] defineda new graph invariant which is named the Sombor index $\mathrm{SO}(G)$ of agraph $G$ and is computed via the expression \[  \mathrm{SO}(G) = \sum_{u \sim v} \sqrt{\mathrm{deg}(u)^2 + \mathrm{deg}(v)^2}, \] where $\mathrm{deg}(u)$ represents the degree of the vertex $u$ in $G$ andthe 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 thegreedy tree attains the minimum Sombor index on the set $\mathcal{T}_D$.

Greedy trees have minimum Sombor indices