香蕉树的Hosoya指标和Merrifield-Simmons指标的显式公式  

Explicit Formulas of Hosoya Index and Merrifield-Simmons Index of Banana Trees

作　　者：杨利民 Yang Limin(College of Mathematics and Computer,Dali University,Dali,Yunnan 671003,China)

机构地区：[1]大理大学数学与计算机学院,云南大理671003

出　　处：《大理大学学报》2021年第12期1-4,共4页Journal of Dali University

基　　金：大理大学高层次人才科研启动费项目(KY0719203410)。

摘　　要：Hosoya指标和Merrifield-Simmons指标是化学图论中两个重要的拓扑参数。设G_(1),G_(2),…,G_(n)是一族互不相交的星形图,通过加入一个新的顶点,并把它连接到每一个星形图Gi的一个悬挂顶点上,那么所得到的树叫做香蕉树。通过图的分支分析法,得到香蕉树的S^((n))-因子计数公式,进一步导出香蕉树的Hosoya指标的显式公式。最后,采用同样的思想,香蕉树的Merrifield-Simmons指标的显式公式被呈现。Hosoya index and Merrifield-Simmons index are two important topological parameters in chemical graph theory.Let G_(1),G_(2),...,G_(n) be a family of disjoint stars,the tree obtained by joining a new vertex to one pendant vertex of each star Gi is called a banana tree.In this paper,by analyzing components in graph theory,the number of all S^((n))-factors of any banana tree is derived,further,explicit formula of Hosoya index of a banana tree is gained.Finally,in a similar vein,explicit formula of Merrifield-Simmons index of a banana tree is presented.

关 键 词：香蕉树 S^((n))-因子 HOSOYA指标 MERRIFIELD-SIMMONS指标 

分 类 号：O157.1[理学—数学] O157.5[理学—基础数学]