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...

A method for the calculation of the hyper–Wiener index (WW ) of a benzenoid system B is described, based on its elementary cuts. A pair of elementary cuts partitions the vertices of B into four fragments, possessing nrs , r, s = 1, 2 vertices. WW is equal to the sum of terms of the form n11 n22 + n12 n21 . The applicability of the method is illustrated by deducing a general expression for WW of...

In this paper, the infra-red absorption spectra of a number of crystalline natural estrogens are presented and considered in relation to chemical structure. As a group, the natural estrogens are distinguished chemically from other steroids by the benzenoid structure of Ring A, which gives rise to certain infra-red absorption bands by which their spectra may be differentiated from those of other...

Tessellations of kekulenes and cycloarenes have a lot potential as nanomolecular belts for trapping transporting heavy metal ions chloride because they the best electronic properties pore sizes. The aromaticity, superaromaticity, chirality, novel electrical magnetic class known been subject several experimental theoretical studies. Through topological computations superaromatic structures with ...

 In this paper we study the relative entropy rate between a homogeneous Markov chain and a hidden Markov chain defined by observing the output of a discrete stochastic channel whose input is the finite state space homogeneous stationary Markov chain. For this purpose, we obtain the relative entropy between two finite subsequences of above mentioned chains with the help of the definition of...

In this paper, Kekule structures of benzenoid chains are considered. It has been shown that the coefficients of a B_n (x) Morgan-Voyce polynomial equal to the number of k-matchings (m(G,k)) of a path graph which has N=2n+1 points. Furtermore, two relations are obtained between regularly zig-zag nonbranched catacondensed benzenid chains and Morgan-Voyce polynomials and between regularly zig-zag ...