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

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

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

Minimal configurations and interlacing

A graph is singular of nullity n if zero is an eigenvalue of its adjacency matrix with multiplicity n. A subgraph that forces a graph to be singular is called a minimal configuration. We show various properties of minimal configurations.peer-reviewe