The Hosoya Index Order of Three Type of Special Graphs

The Hosoya index of a graph is defined as the summation of the coefficients of the matching polynomial of a graph. In this paper, we give an explicit expression of the Hosoya index for the graphs \( C(n, v_1v_i) \), \( Q(n, v_1v_s) \), and \( D(s, t) \), and also characterize the extremal graphs with respect to the upper and lower bounds of the Hosoya index of these graphs. In particular, we provide the Hosoya index order for the graphs \( C(n, v_1v_i) \) and \( Q(n, v_1v_s) \), respectively.