Kekulé structures of square–hexagonal chains and the Hosoya index of caterpillar trees

Let RnRn be a square–hexagonal chain. In this paper, we show that there exists a caterpillar tree TnTn such that the number of Kekulé structures of RnRn is equal to the Hosoya index of TnTn. Since both hexagonal chains and polyomino chains can be viewed as special square–hexagonal chains, our result generalizes the corresponding results for hexagonal chains (Gutman, 1977) and polyomino chains (Liand Yan, 2012).