基于拉格朗日乘数法的小直径单圈图的Szeged指数研究  

A Study of the Szeged Index of Small-Diameter Unicyclic and Bicyclic Maps Based on the Lagrange Multiplier Method

作　　者：钱儒亮 田志伟 钟珍妮 Qian Ruliang;Tian Zhiwei;Zhong Zhenni(School of Mathematics and Statistics,Qinghai University for Nationalities,Xining,China;School of Civil and Traffic Engineering,Qinghai University for Nationalities,Xining,China)

机构地区：[1]青海民族大学数学与统计学院,青海西宁 [2]青海民族大学土木与交通工程学院,青海西宁

出　　处：《科学技术创新》2025年第1期214-217,共4页Scientific and Technological Innovation

摘　　要：本文探讨了化学图论中Szeged指数在直径为3的小直径单圈图中的极值情况。Szeged指数作为描述分子拓扑结构的重要工具,在生物化学领域具有广泛应用。通过定义及性质介绍,我们计算并证明了这些特殊图形的Szeged指数极值的存在性和唯一性。这些研究结果不仅提供了对Szeged指数性质和应用的重要见解,也为相关问题的解决提供了启示。随着图论的发展,越来越多的图论指数被提出并应用于不同领域,Szeged指数作为其中的重要指数,有助于深入理解图的结构和复杂性。In this paper,we explore the extremes of the Szeged exponent in chemical graph theory for small-diameter one-circle graphs of diameter 3.The Szeged exponent has a wide range of applications in biochemistry as an important tool for describing the topology of molecules.By means of definitions and introduction of properties,we calculate and prove the existence and uniqueness of the extreme values of the Szeged index for these particular graphs.These findings not only provide important insights into the properties and applications of Szeged exponents,but also shed light on related problems.With the development of graph theory,more and more graph-theoretic indices have been proposed and applied in different fields,and Szeged index,as one of the important indices,helps to deeply understand the structure and complexity of graphs.

关 键 词：Szeged指数 拉格朗日乘数法 单圈图 

分 类 号：O157.5[理学—数学]