Structural codes vis-a-vis structural counts, like polynomials of a molecular graph, are important in computing graph-theoretical descriptors which are commonly known as topological indices. These indices are most important for characterizing carbon nanotubes (CNTs). In this paper we have computed Sadhana index (Sd) for phenylenes and their hexagonal squeezes using structural codes (counts). Sa...

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...

We show that the molecular graph G of a benzenoid hydrocarbon admits an isometric embedding into the Cartesian product of three trees T1, T2, and T3 defined by three directions of the host hexagonal grid. Namely, to every vertex V of G one can associate an ordered triplet (V1, V2, V3) with Vi being a vertex of Ti (i ) 1, 2, 3), such that the graph-theoretic distance between two vertices u, V of...

Application of topological properties and graph theory to benzenoid hydrocarbons allowed us to construct an effective approach interpreting ring current formation in molecules when exposed to an external magnetic field. Transformation of unexcited canonical structures for molecules of 34 benzenoid hydrocarbons into circuit structures and then to directed circuit structures allowed us to define ...

The importance of caterpillar trees in the topological theory of benzenoid systems lies in the following. Let B be a non-branched cata-condensed benzenoid hydrocarbon (that is a hydrocarbon containing linearly and angularly condensed rings). If we associate a symbol L to each linearly condensed ring (and also to the two terminal ones) and a symbol A to each angularly condensed ring, then the so...

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 ...

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 ...

A structure-descriptor EE, recently proposed by Estrada, is examined. If λ1, λ2, . . . ,λn are the eigenvalues of the molecular graph, then EE = n ∑ i=1 eλi . In the case of benzenoid hydrocarbons with n carbon atoms and m carbon-carbon bonds, EE is found to be accurately approximated by means of the formula a1 n cosh (√ 2m/n ) +a2, where a1 ≈ 1.098 and a2 =−0.64 are empirically determined fitt...

Recent experimental methods have made it possible to synthesize very large benzenoid molecules, sometimes referred to as “graphenes”.1–3 These have found unprecedented applications as organic materials for electronic and optoelectronic devices.2,3 As large benzenoid systems have countless possible isomers,4–6 it is a task of theoretical chemistry to help indicate those species that may possess ...

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...