New General Formulations for Constant-Isomer Series of Polycyclic Benzenoids

Abstract

Constant-isomer series have the same number of isomers and corresponding membership topology at each stage of the circumscribing process. New general formulas which generate the first generation molecular formulas to all constant isomer benzenoid hydrocarbons are presented for the first time. These general formulas along with our recursion equations allow one to obtain all the molecular formulas of benzenoid constant-isomer series. These general formulas are more convenient than those previously derived by Cyvin and coworkers based on the Harary/Harborth upper/lower bounds. At the same time, these general formulas also identify the various topological subclasses of these constant-isomer series.

Key Words:

• benzenoid hydrocarbons
• constant-isomer series
• topological subclasses
• general molecular formulas