The largest Hosoya index of (n,n+1)(n,n+1)-graphs

The Hosoya index of a graph is defined as the total number of its matchings. In this paper, we obtain that the largest Hosoya index of (n,n+1)(n,n+1)-graphs is f(n+1)+f(n−1)+2f(n−3)f(n+1)+f(n−1)+2f(n−3), where f(n)f(n) is the nnth Fibonacci number, and we characterize the extremal graphs.