AI 中文总结
研究关于简单图的缩减索姆博尔指数\(DSO\)，通过几个基本图参数和拓扑指数建立新精确界，严格规定等式条件，深化理论理解并为数学化学跨学科应用提供分析工具。
AI 中文摘要
简单图\(G\)的缩减索姆博尔指数\((DSO)\)是最近引入的基于度的拓扑指数，定义为\[ DSO(G)= \sum_{uv\in E(G)} \frac{\sqrt{d_u^2+d_v^2}} {d_u+d_v} \] 本文根据几个基本图参数和著名拓扑指数建立了\(DSO\)指数的新精确界，严格规定了等式条件，深化了对\(DSO\)指数的理论理解，为数学化学的跨学科应用提供了有力分析工具。
英文摘要
The Diminished Sombor index $(DSO)$ of a simple graph $G$ is a recently introduced degree-based topological index, defined as \[ DSO(G)= \sum_{uv\in E(G)} \frac{\sqrt{d_u^2+d_v^2}} {d_u+d_v} \] In this paper, we establish a collection of new sharp bounds for the $DSO$ index in terms of several fundamental graph parameters and well-known topological indices. In all cases, the proposed bounds rigorously specify the equality conditions, thereby providing a complete characterization of the extremal graphs. These findings deepen the theoretical understanding of the $DSO$ index and provide powerful analytical tools for interdisciplinary applications in mathematical chemistry.
