On the number of Kekulé structures of fluoranthene congeners

Abstract

The Kekulé 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 congeners having exactly t Kekulé structures. Three classes of Kekuléan fluoranthenes are distinguished: i) φ 0 - fluoranthene congeners in which neither the male nor the female benzenoid fragment has Kekulé structures, ii) φ m - fluoranthene congeners in which the male benzenoid fragment has Kekulé structures, but the female does not, and iii) φ fm - fluoranthene congeners in which both the male and female benzenoid fragments have Kekulé structures. Necessary and sufficient conditions are established for each class, φ = φ 0, φ m, φ fm, such that for a given positive integer t, there exist fluoranthene congeners inφ with the property K = t. © 2010 Copyright (CC) SCS.