Volume 35 • Number 4 • 2012   • On the Ordering of Trees by the Two Indices Chengfu Ye and Zhiquan Hu Abstract. The Merrifield-Simmons index of a graph is defined as the total number of the independent sets of the graph and the Hosoya index of a graph is defined as the total number of the matchings of the graph. In this paper, among all the trees with $n$ vertices and $k$ pendent vertices, we determine the trees with the first $[{n-k+1}/{2}]$ largest Merrifield-Simmons index and the trees with the first $[{n-k+1}/{2}]$ smallest Hosoya index. 2010 Mathematics Subject Classification: 11B39, 05C05. Full text: PDF