Kekulé structures of polyomino chains and the Hosoya index of caterpillar trees

Let HH be a hexagonal chain. Gutman [I. Gutman, Topological properties of benzenoid systems, Theor. Chim. Acta, 45 (1977), 307–315.] proved that there exists a caterpillar tree T(H)T(H) such that the number of Kekulé structures of HH is equal to the Hosoya index of T(H)T(H). In this note, we show that, for a polyomino chain QQ, there exists a corresponding caterpillar tree C(Q)C(Q) such that the number of Kekulé structures of QQ is equal to the Hosoya index of C(Q)C(Q).