We present an improved parallel algorithm for the enumeration of fixed benzenoids Bh containing h hexagonal cells. We can thus extend the enumeration of Bh from the previous best h = 35 up to h = 50. Analysis of the associated generating function confirms to a very high degree of certainty that Bh ∼ Aκh/h and we estimate that the growth constant κ = 5.161930154(8) and the amplitude A = 0.280849...

Zagreb indices belong to better known and better researched topological indices. We investigate here their ability to discriminate among benzenoid graphs and arrive at some quite unexpected conclusions. Along the way we establish tight (and sometimes sharp) lower and upper bounds on various classes of benzenoids.

We make use of the classical correspondence between Kekulé structures and lattice paths to obtain explicit formulas for the Pauling bond order of edges in benzenoid parallelograms. These formulas are further used to establish the average π-electron content of hexagonal rings in such benzenoids. We then compare this quantity with the atom-based π-electron content of rings, and study the local an...

zagreb indices belong to better known and better researched topological indices. weinvestigate here their ability to discriminate among benzenoid graphs and arrive at some quiteunexpected conclusions. along the way we establish tight (and sometimes sharp) lower andupper bounds on various classes of benzenoids.

Many chemical properties of benzenoid hydrocarbons can be understood in terms of the maximum number of mutually resonant hexagons, or Clar number, of the molecules. Hansen and Zheng (1994) formulated this problem as an integer program and conjectured, based on computational results, that solving the linear programming relaxation always yields integral solutions. We prove this conjecture showing...

The enhanced stability of bent or kinked polycyclic benzenoids over linear ones is well established, phenanthrene and anthracene being archetypal representatives. The question why kinked is more stable than linear is, however, still a matter of discussion. Recently, it has been proposed that H-H bonding interactions between the two hydrogen atoms in the bay region of phenanthrene are responsibl...

Eric Clar’s qualitative ideas for benzenoids are described in application to various novel nanostructures: graphene, edges in graphene, carbon nanotubes, carbon nanocones, and carbon nanotori. The specially singled out most highly aromatic species with Clar structures consisting entirely of aromatic sextets are proposed to be termed “claromatic”. Several such claromatic nanostructures are ident...

The enumeration of Kekule structures has fasci­ nated several researchers since the first systematic studies of benzenoids in terms of graph theory [1-9] , Apart from the recognized importance of Kekule structures in organic and physical chemistry they also have purely mathematical interest. Refer­ ence is made to a recent article in the present jo u r ­ nal [10] along with the bibliography the...