In this paper the Clar covering polynomial of a hexagonal system is introduced. In fact it is a kind of F polynomial [4] of a graph, and can be calculated by recurrence relations. We show that the number of aromatic sextets (in a Clar formula), the number of Clar formulas, the number of Kekule structures and the first Herndon number for any Kekulean hexagonal system can be easily obtained by it...

The interaction of delocalized π-electrons with molecular vibrations is key to charge transport processes in π-conjugated organic materials based on aromatic monomers. Yet the role that specific aromatic motifs play on charge transfer is poorly understood. Here we show that the molecular edge topology in charged catacondensed aromatic hydrocarbons influences the Herzberg-Teller coupling of π-el...

We consider a family of structurally closely related fully-benzenoid hydrocarbons of increasing number of fused benzene rings. Local and global aromatic properties of such molecules are investigated with a particular interest in investigating the role of the finite size of such molecules in modelling the high-polymer or even graphite. An interesting alternation of local properties for benzene r...

The atom-bond connectivity (ABC) index is a recently introduced topological index, defined as ABC(G) = ∑ uv∈E(G) √ du+dv−2 dudv , where du (or dv) is the degree the vertex u (or v). The ABC index of benzenoid systems and phenylenes are computed, a simple relation is established between the atom-bond connectivity index of a phenylene and the corresponding hexagonal squeeze in this paper. Mathema...

Kekule structures are transformed into the subspace of their double bonds to yield the correspondilng factor graphs, orig.inally called submolecules (8. E 1Bas i 1, Internat. J. Quantum Chem. 21 (1982) 771). A graiph-theoretical analysis of factor graphs is presented for certain classes o,f benzeno1i:d hydrocarbons. Such an analysis led to expressions for .the construction of sextet polynomials...

A number of mathematical relations for the sextet polynomial are derived. A graph has been introduced (the so called C-graph), representing those properties of a benzenoid system which are essential in the sextet theory of Clar. The main structural properties of the C-graph are determined. The obtained results contribute towards a better understanding of the algebraic and combinatorial backgrou...

The title compound, C(20)H(32)N(2)O(2)S(2), has been synthesized by the reaction of α-methyl-sulfanylcyclo-dodeca-none and p-toluene-sulfonyl-hydrazine. In the crystal structure, the conformation of the non-benzenoid ring is [3333] and the methyl-sulfanyl group is in the α-side exo position. The mol-ecules are linked by inter-molecular N-H⋯S hydrogen bonds.

A hexagonal patch is a plane graph in which inner faces have length 6, inner vertices have degree 3, and boundary vertices have degree 2 or 3. We consider the following counting problem: given a sequence of twos and threes, how many hexagonal patches exist with this degree sequence along the outer face? This problem is motivated by the study of benzenoid hydrocarbons and fullerenes in computati...