Quantitative Correlation of Randić Indices and Adjacency Matrixes With Dewar Resonance Energy of Annulene Compounds

Topological indices are the numerical value associated with chemical constitution purporting for correlation ofchemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is adelightful playground for the exploration of proof techniques in Discrete Mathematics and its results haveapplications in many areas of sciences. One of the useful indices for examination of structure-proeprtyrelationship is Randić index. In this study, is represented the relationship between the Randić index and thedeterminants of the adjacency matrix to the Dewar resonance energy (DRE) of annulene compounds by usingab-initio calculations (B3LYP/6-31G*). The alternative double bonds and conjugation are one of the mainproperties in annulene compounds. DRE is the quantity which allows one to account for the effects of cyclicelectron delocalization and thus serves as a measure of the aromatic stabilization of an annulene molecularentity. For calculation the Dewar resonance energy (DRE) of the compounds could use the equation of DRE.The interesting results of concerning among DRE and the above indices are presented.