Abstract:

Hosoya index and Merrifield-Simmons index are two important topological parameters in chemical graph theory. Let G1， G2， ...，Gn 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.

Key words: banana tree, S （n ）-factor, Hosoya index, Merrifield-Simmons index