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