毛虫形图中第一类和第二类Zagreb指数的研究与应用  

Study and Application of Type I and Type II Zagreb Indices in Caterpillar Shape Diagrams

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2期221-224,共4页Scientific and Technological Innovation

摘　　要：本研究聚焦于探索毛虫形图中第一类和第二类Zagreb指数的基本性质。这些指数在化学、社会网络和生物网络等领域具有广泛应用,与图的能量、光谱半径等密切相关,为理解复杂网络提供新视角。毛虫形图作为特殊树状图,在化学图论中常用于模拟有机分子结构。通过计算和证明指数的极值存在性和唯一性,本研究拓展了这些指数在毛虫形图中的应用,有助于深入理解指数的性质和为相关问题的解决提供启示。这一研究成果对未来的图论研究和指数应用具有积极意义,推动着该领域的进一步发展。This study focuses on exploring the fundamental properties of Type I and Type II Zagreb indices in caterpillar-shaped graphs.These indices have a wide range of applications in the fields of chemistry,social networks and biological networks,and are closely related to the energy and spectral radius of the graphs,providing new perspectives for understanding complex networks.Caterpillar-shaped diagrams,as special tree diagrams,are often used in chemical graph theory to model the structure of organic molecules.By calculating and proving the existence and uniqueness of the extremes of the indices,this study expands the application of these indices in caterpillar-shaped graphs,which helps to deeply understand the nature of the indices and provides insights into the solution of related problems.The results of this research are of positive significance for future graph theory research and exponential applications,driving further development in this field.

关 键 词：毛虫形图 第一类Zagreb指数 第二类Zagreb指数 

分 类 号：O157.5[理学—数学]