论文标题
贪婪的树木有最低的Sombor指数
Greedy trees have minimum Sombor indices
论文作者
论文摘要
最近，古特曼[Match Commun。数学。计算。化学86（2021）11-16]定义了一个新的图形不变式，该图被称为sombor索引$ \ mathrm {so}（g）agragh $ g $的$，并通过expression \ [ \ Mathrm {so}（g）= \ sum_ {对相邻顶点$ u $和$ v $。在这里，我们考虑了所有具有指定度序列$ d $的树$ \ Mathcal {t} _d $的集合，并表明贪婪的树达到了集合$ \ MATHCAL {T} _D $的最低Sombor索引。
Recently, Gutman [MATCH Commun. Math. Comput. Chem. 86 (2021) 11-16] defined a new graph invariant which is named the Sombor index $\mathrm{SO}(G)$ of a graph $G$ 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 $G$ 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 $\mathcal{T}_D$.
