The Merrifield–Simmons Indices and Hosoya Indices of Trees with k Pendant Vertices

摘要

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, we characterize the trees with maximal Merrifield–Simmons indices and minimal Hosoya indices, respectively, among the trees with k pendant vertices.