On the number of Kekulé structures of fluoranthene congeners

Abstract

The Kekul? structure count K of fluoranthene congeners is studied. It is shown that for such polycyclic conjugated ?-electron systems, either K = 0 or K ? 3. Moreover, for every t ? 3, there are infinitely many fluoranthene congeners having exactly t Kekul? structures. Three classes of Kekul?an fluoranthenes are distinguished: (i) ?0 - fluoranthene congeners in which neither the male nor the female benzenoid fragment has Kekul? structures, (ii) ?m - fluoranthene congeners in which the male benzenoid fragment has Kekul? structures, but the female does not, and (iii) ?fm - fluoranthene congeners in which both the male and female benzenoid fragments have Kekul? structures. Necessary and sufficient conditions are established for each class, ? = ?0, ?m, ?fm, such that for a given positive integer t, there exist fluoranthene congeners in ? with the property K = t.