Catacondensed Benzenoids

Abstract

The single linear and zigzag chains are treated in Chapter 4. It is reasonable to give Gordon and Davison (1952) credit for eqn. (4.2) therein, although it has certainly been discovered independently many times; cf. the simple considerations of Section 4.3 (Cyvin and Gutman 1986a). The identification of the number of Kekulé structures (K) for a single zigzag chain with the Fibonacci numbers was also mentioned already by Gordon and Davison (1952). The explicit form corresponding to Binet’s formula was first given by Yen (1971) and independently by Cvetković and Gutman (1974). Cyvin (1983a) re-derived the connection between Fibonacci numbers and the number of Kekulé structures for single zigzag chains, and supplemented the treatment by group-theoretical considerations of symmetry. A treatise on three connections between Fibonacci numbers and Kekulé structures is due to Balaban and Tomescu (1984); see also Hosoya (1973).