A Kekulé structure basis for phenylenes

By means of Kekulé structures and, in particular, their count K, many properties of benzenoid molecules can be rationalized. The analogous properties of non-benzenoid polycyclic conjugated molecules require the consideration of some, but not all, Kekulé structures, whose number is the precisely defined and long time known 'algebraic structure count' ASC. In the general case it is not known how to construct a Kekulé structure basis for non-benzenoid molecules, consisting of ASC Kekulé structures, ASC≤K. We now offer a solution of this problem for phenylenes and point out some applications.