On the number of kekulé structures of unbranched cata-condensed benzenoid chains

✍ Scribed by T.P. Živković; N. Trinajstić

• Publisher: Elsevier Science
• Year: 1987
• Tongue: English
• Weight: 174 KB
• Volume: 136
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(87)80432-3

✦ Synopsis

It is known that an alternative algorithm to the Gordon-Davidson algorithm for counting the Kekule valence structures of catacondensed non-branched benzenoid hydrocarbons is a reformulation of the original algorithm.

Recently an alternative algorithm [ 1,2] to the Gordon-Davison (GD) algorithm [ 31 for counting the KekulC valence structures of data-condensed benzenoid chains has been proposed. In this note we show that this alternative proposal is a reformulation of the original algorithm.

Let us first briefly illustrate the use of the GD algorithm: A hexagon at the end of the chain is chosen and inserted (because the KekulC number for benzene is 2); write 3 in the adjacent ring (because the KekulC number for naphthalene is 3). Subsequent rings if fused linearly increase the inscribed value by + 1, but if the direction of fusion has changed one has to add not + 1, but the value in the preceding ring. The process continues by adding this number for each subsequent linearly annelated ring until the next change of fusion direction occurs when the process is repeated in the same fashion. The process ends when we have exhausted all available rings. An illustrative example is shown below.