On the Hosoya Indices of Bicyclic Graphs with Small Diameter - Tingzeng Wu; Yong Yu (Journal of Chemistry, 2021)
Let G be a graph. The Hosoya index of G, denoted by zG, is defined as the total number of its matchings. The computation of zG is NP-Complete. Wagner and Gutman pointed out that it is difficult to obtain results of the maximum Hosoya index among tree-like graphs with given diameter. In this paper, we focus on the problem, and a sharp bound of Hosoya indices of all bicyclic graphs with diameter of 3 is determined.