Perfect Matchings in Polyhexes, or Recent Graph-theoretical Contributions to Benzenoids

After an introduction on the history of polycyclic aromatic compounds, recent advances in the theory of benzenoids are briefly reviewed. Then using systems with 4, 5, or 6 benzenoid rings for illustration, the partition of the P π-electrons among the rings of the benzenoid is presented, followed by a different way of examining the distribution of these π-electrons which is called the signature of the benzenoid, consisting in six integers from s6 to s1. The P π-electrons are divided between the two sums s6 + s5 + s2 + s1 and s4 + s3 characterizing thereby the closeness of benzenoids to all-resonant structures according to Clars theory.