Perfect Matchings in Polyhexes, or Recent Graph-theoretical Contributions to Benzenoids 1

Abstract: 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. ThePπ-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. Key Words: Perfect matchings (1-factors, resonance structures, or Kekulé structures); polycyclic aromatic hydrocarbons (polyhexes or benzenoids); isoarithmic benzenoids