On the number of Kekulé structures of fluoranthene congeners

The Kekule structure count K of fluoranthene congeners is studied. It is shown that for such polycyclic conjugated π-electron systems, either K = 0 or K ≥ 3. Moreover, for every t ≥ 3, there are infinitely many fluoranthene con- geners having exactly t Kekule structures. Three classes of Kekulean fluoran- thenes are distinguished: i) Φ0 - fluoranthene congeners in which neither the male nor the female benzenoid fragment has Kekule structures, ii) Φm - fluo- ranthene congeners in which the male benzenoid fragment has Kekule structures, but the female does not, and iii) Φfm - fluoranthene congeners in which both the male and female benzenoid fragments have Kekule structures. Necessary and sufficient conditions are established for each class, Φ = Φ0, Φm, Φfm, such that for a given positive integer t, there exist fluoranthene congeners in Φ with the property K = t.