The Maximal Merrifield-Simmons Indices and Minimal Hosoya Indices of Unicyclig Graphs

摘要

The Merrifield-Simmons index of a graph is denned 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 unicyclic graphs with maximal Merrifield-Simmons indices and minimal Hosoya indices, respectively, among all unicyclic graphs witli n vertices and k pendent vertices.