Can the John Sachs Theorem Be Extended to Clar Covers?

We demonstrate on multiple examples that Zhang-Zhang (ZZ) polynomials of benzenoids with k peaks and k valleys can be computed as determinants of certain k k matrices. The results bear a striking similarity to the John-Sachs theorem, suggesting that an extension of this theorem to Clar covers may exist. The diagonal elements of the generalized John-Sachs matrices are given by the ZZ polynomials of the corresponding path regions; the off-diagonal elements meaning is more obscure and remains to be elucidated. Several detected difficulties suggest that the postulated generalization of the John-Sachs theorem to Clar covers might be a non-Trivial and challenging task.