论文标题
在具有给定连接性和桥梁数量的图形索引上
On the Sombor index of graphs with given connectivity and number of bridges
论文作者
论文摘要
最近在2021年，古特曼（Gutman）引入了一个基于学位的拓扑指数的Sombor指数。已经表明，Sombor指数有效地模拟了化合物的热力学特性。假设$ \ mathbb {b} _n^k $（resp。$ \ mathbb {v} _n^k $）包括所有图形，带有订单$ n $，$ n $，$ n $具有桥梁数量（rids.vertex-connectivity）$ k $。 Horoldagva＆Xu（2021）表征了图形，以$ \ MATHBB {B} _n^K $中的最大SOMBOR索引。本文的特征是在$ \ mathbb {b} _n^k $中实现最低SOMBOR索引的图表。 $ \ mathbb {b} _n^k $中的图形上的某些辅助操作被引入并用于表征。此外，我们表征了在$ \ mathbb {v} _n^k $中获得最大SOMBOR索引的图形。最终提出了这项工作，自然而然地提出了开放问题。
Recently in 2021, Gutman introduced the Sombor index of a graph, a novel degree-based topological index. It has been shown that the Sombor index efficiently models the thermodynamic properties of chemical compounds. Assume $\mathbb{B}_n^k$ (resp. $\mathbb{V}_n^k$) comprises all graphs with order $n$ having number of bridges (resp. vertex-connectivity) $k$. Horoldagva & Xu (2021) characterized graphs achieving the maximum Sombor index of graphs in $\mathbb{B}_n^k$. This paper characterizes graphs achieving the minimum Sombor index in $\mathbb{B}_n^k$. Certain auxiliary operation on graphs in $\mathbb{B}_n^k$ are introduced and employed for the characterization. Moreover, we characterize graphs achieving maximum Sombor index in $\mathbb{V}_n^k$. ome open problems, which naturally arise from this work, have been proposed at the end.
