Recursive Formulae for Enumeration of LM-Conjugated Circuits in Structurally Related Benzenoid Hydrocarbons

Abstract

The linearly independent and minimal conjugated (LM-conjugated) circuits of benzenoid hydrocarbons play the central role in the conjugated circuit model. For a general case, the enumeration of LM-conjugated circuits may be tedious as it requires construction of all Kekule structures. In our previous work, a recursive method for enumeration of LM-conjugated circuits of benzenoid hydrocarbons was established. In this paper, we further extend the recursive formulae for enumerations of LM-conjugated circuits for both catacondensed benzenoid hydrocarbons and some families of structurally related pericondensed benzenoid hydrocarbons.