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

Let H 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 ) such that the number of Kekulé structures of H is equal to the Hosoya index of T ( H ) . In this note, we show that, for a polyomino chain Q , there exists a corresponding caterpillar tree C ( Q ) such that the number of Kekulé structures of Q is equal to the Hosoya index of C ( Q ) .