Mohammad Hadi Akhbari - Islamic Azad University
Fateme Movahedi - Golestan University

The Hosoya index Z(G) of a graph G is the total number of matchings in it. In this paper, the recursive formulas of the Hosoya index of semitotal graph Q(G) and total graph T(G) for certain graphs G are obtained. Moreover, we obtain the bounds of the Hosoya index of semitotal and total graphs of a connected graph G.

Hosoya index, Semitotal graph, Total graph