A connection between the Kekulé structures of pentagonal chains and the Hosoya index of caterpillar trees

Abstract Let P n be a pentagonal chain. Motivated by the work of Gutman (1977), this paper shows that for a hexagonal chain H , there exists a caterpillar tree T ( H ) such that the number of Kekule structures of H is equal to the Hosoya index of T(H). In this paper, we show that for a pentagonal chain P n with even number of pentagons, there exists a caterpillar tree T n 2 such that the number of Kekule structures of P n is equal to the Hosoya index of T n 2 . This result can be generalized to any polygonal chain Q n with even number of odd polygons.