The Largest n − 1 Hosoya Indices of Unicyclic Graphs

Abstract

The Hosoya index Z(G) of a graph G is defined as the total number of edge independent sets of G. In this paper, we extend the research of [J. Ou, On extremal unicyclic molecular graphs with maximal Hosoya index, Discrete Appl. Math. 157 (2009) 391–397.] and [Y. Ye, X. Pan, H. Liu, Ordering unicyclic graphs with respect to Hosoya indices and Merrifield-Simmons indices, MATCH Commun. Math. Comput. Chem. 59 (2008) 191–202.] and order the largest n − 1 unicyclic graphs with respect to the Hosoya index.