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

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

Computing the dependence of graph energy on nullity: The method of siblings

The energy of a graph is the sum of absolute values of its eigenvalues. The nullity of a graph is the algebraic multiplicity of number zero in its spectrum. The dependence of graph energy on nullity is of importance in chemical applications. In this paper we present a method by means of which this dependence can be calculated

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

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