Some Topological Properties of Benzenoid Systems

In recent years conjugated molecules have been intensely studied by means of graph theory1 and a number of their chemical and physical properties could be described and/or predicted. The aim of the present note is to analyze a special class of molecular graphs2 which are of doubtless importance for chemistry since they represent benzenoid hydrocarbons

A Graph-Theoretical Study of Conjugated Systems Containing a Linear Polyene Fragment

Conjugated molecules containing a linear polyene fragment are studied using graph theory. It is shown that the characteristic polynomials of the molecular graphs of .these sy&tems fulfill a common recurrence relation and have, therefore, a common general form. The spectra of 10 classes of isuch graphs are obtained in analytical form. These spectra are mutually related and are also related to the spectrum of cycles (which are molecular graphs of annulenes). From the spectra obtaililed analytical expressions for total n:-electron energy, HOMO-LUMO separation, etc. are deduced

The Number of Kekule Structures in Conjugated Systems Containing a Linear Polyacene Fragment

The number of Kekule structures of all conjugated systems containing a linear polyacene chain of length n is a linear function of the parameter n and is given by eq. (8)

Some Less Familiar Properties of Randić Index

Several mathematically relevant properties of the Randić connectivity index, that may be less familiar to the chemical community, are outlined and commented. This work is licensed under a Creative Commons Attribution 4.0 International License

A Method for Enumeration of the Algebraic Structure Count of Non-Branched Cata-Condensed Molecules

An operator technique for the eI1JUmeration of the algebraic structure coUJilt (ASC) of non-branched cata-condensed molecules has been developed. General formulae for the ASC\u27s of 16 conjugated series have been obtained

A Class of Lower Bounds for Total 7t-Electron Energy of Alternant Conjugated Hydrocarbons

For alternant hydrocarbons whose molecular graphs possess n vertices and m edges Turker recently put forward a lower bound for total n-electron energy (E), namely (1/2) (2 m n)1/2 :$ E (*). The original proof of (*) contains an error. We propose an alternative method for proving (*), which applies to all molecular graphs, except perhaps to some containing very many four membered cycles. As a byproduct, a class of novel lower bounds for E is obtained

Topological Properties of Benzenoid Systems. XXI. Theorems, Conjectures, Unsolved Problems

The main known mathematical results (in the form of 32 theorems and 5 conjectures) about benzenoid systems are collected. A few new results (seven theorems) are proved. Seven unsolved problems are also pointed out. The paper contains results on the basic properties of benzenoid graphs, on the number of Kekule structures and on Clar\u27s resonant sextet formulas

Cyclic Conjugation in Porphin

The paper consists of three parts. In Part A the cyclic conjugation in porphin and some related compounds is examined. It is shown that the Huckel (4m+2)-rule isviolated so that conjugation along both 16-, 17-, 18-, 19- and 20- membered cycles causes stabilization of the rc-electron system of porphin. In Part B some comments on the topological resonance energy method and its application to porphin are given In Part e the four existing methods for the calculation of the effect of cyclic conjugation on the stability of ot-electron systems are compared and their mutual relationship revealed