中文摘要：

Let G be a graph.The Hosoya index Z(G)of a graph G is defined to be the total number of its matchings.In this paper,we characterize the graph with the smallest Hosoya index of bicyclic graphs with given pendent vertices.Finally,we present a new proof about the smallest Hosoya index of bicyclic graphs.

英文摘要：

Let G be a graph. The Hosoya index Z（G） of a graph G is defined to be the total number of its matchings. In this paper, we characterize the graph with the smallest Hosoya index of bicyclic graphs with given pendent vertices. Finally, we present a new proof about the smallest Hosoya index of bicyclic graphs.