New Geometric-Arithmetic Indices

Based on the definition of the general geometric-arithmetic index, this article introduces several new geometric-arithmetic indices (Part One). In Part Three, we have determined the degree of degeneracy of these new invariants and we have designated the first pairs (or subsets) of molecular graphs having the same values of a given geometric-arithmetic index. It appears that in many cases the newly proposed descriptors have a much greater level of uniqueness that the strongly discriminating Balaban J index. In Part Four, we have demonstrated the applicability of these newly defined molecular descriptors for QSPR studies. Namely, we have used them to model certain physicochemical properties of several classes of organic compounds. The results of internal and external validations of the obtained models have indicated that the models based on the new geometric-arithmetic indices have high descriptive and predictive capabilities and are externally stable. Also, these results have testified that the QSPR models based on these new topological indices in many cases outperform models known in the literature. Therefore, it can be speculated that these new geometric-arithmetic indices will be used in future QSPR/QSAR studies.