论文标题
在Sombor指数上的空旷问题的证明
Proof of an open problem on the Sombor index
论文作者
论文摘要
SOMBOR索引是基于几何的描述符之一，其定义为$$ SO（g）= \ sum_ {uv \ in E（g）} \ sqrt {d^{2}（2}（2}（u）+d^{2} {2} {2}（v）（v）（v）}，$ d where $ d（u）$ d（u）$ d（us）$ d（usd. $ d（us） $ g $。在本说明中，我们确定了最大值和最小图，相对于具有顶点连接性（分别为边缘连接性）的一组图表中的SOMBOR索引，最多$ k $在Hayat和Rehman提出的Sombor索引上解决了一个开放问题，[在Sombor索引上提出了图形索引索引索引索引索引，并具有给定数量的CUT-VERTICES，CUT-VERTICES，匹配的Muncum。数学。计算。化学89（2023）437--450]。对于上文的一些结论，我们给出一些反例。最后，我们通过回归建模和SOMBOR指数进行了QSPR分析。
The Sombor index is one of the geometry-based descriptors, which was defined as $$SO(G)=\sum_{uv\in E(G)}\sqrt{d^{2}(u)+d^{2}(v)},$$ where $d(u)$ (resp. $d(v)$) denotes the degree of vertex $u$ (resp. $v$) in $G$. In this note, we determine the maximum and minimum graphs with respect to the Sombor index among the set of graphs with vertex connectivity (resp. edge connectivity) at most $k$, which solves an open problem on the Sombor index proposed by Hayat and Rehman [On Sombor index of graphs with a given number of cut-vertices, MATCH Commun. Math. Comput. Chem. 89 (2023) 437--450]. For some of the conclusions of the above paper, we give some counterexamples. At last, we give the QSPR analysis with regression modeling and Sombor index.
