RECURSIVE METHOD FOR ENUMERATION OF LINEARLY INDEPENDENT AND MINIMAL CONJUGATED CIRCUITS OF BENZENOID HYDROCARBONS

The linearly independent and minimal conjugated (LM-conjugated) circui ts of benzenoid hydrocarbons (BHs) play the central role in the conjug ated circuit model. For a general case, the enumeration of LM-conjugat ed circuits of BHs may be tedious as it requires construction of all K ekule structures. In the present paper, we investigate the properties and the construction of minimal conjugated circuits of BHs, and give t he necessary and sufficient condition for a set of conjugated circuits of a BH to be linearly independent and minimal. Furthermore, we estab lish some recursive relations for enumeration of LM-conjugated circuit s for several classes of BHs, one class of which consists of all the B Hs containing no crown subunit. By these recursive relations, the summ ation expressions of LM-conjugated circuits (LMC-expressions) of the s everal classes of BHs can be directly obtained from the LMC-expression s and the Kekule structure counts of their subgraphs.