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

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.