Perfect Matchings in Polyhexes, or Recent Graph-theoretical Contributions to Benzenoids
Alexandru T. Balaban (Texas A&M University at Galveston, USA)
Milan Randić (National Institute of Chemistry, Slovenia)
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. 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.
Keywords: Clar structures, isoarithmic benzenoids, perfect matchings (1-factors, resonance structures, or Kekul'e structures), polycyclic aromatic hydrocarbons (polyhexes or benzenoids)
Categories: G.2.2, J.2