The Largest $n-1$ Hosoya Indices of Unicyclic Graphs

Guihai Yu, Lihua Feng, Aleksandar Ilić

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.