On Relationships of Eigenvalue–Based Topological Molecular Descriptors

Abstract

Three eigenvalue-based topological molecular descriptors are compared using several datasets of alkanes. Two of them are well-known and frequently employed in various QSPR/QSAR investigations, and third-one is a newly derived whose predictive potential is yet to be proven. The relations among them are found and discussed. Structural parameters that govern these relations are identified and the corresponding formulas based on multiple linear regression have been obtained. It has been shown that all three investigated indices are encoding almost the same structural information of a molecule. They differ only by the extent of the sensitivity on a structural branching of a molecule and on the number of non-bonding molecular orbitals.

Resolvent Energy and Estrada Index of Benzenoid Hydrocarbons

“…Extraordinary linear relationships between resolvent energy and Estrada index are identified in benzenoid hydrocarbons, both in catacondensed and pericondensed molecules. This finding validates the approximative formula connecting the resolvent energy and the Estrada index, established in the paper (Redžepović and Furtula 2020). Also, these two descriptors show similar predictive potential in the case of benzenoid hydrocarbons.…”

Effect of a Ring onto Values of Eigenvalue–Based Molecular Descriptors

“…This implies that in comparison with the energy of a graph, the resolvent energy, and the Estrada index are gathering completely different structural details. Although the previous investigations detected similar behavior of the resolvent energy and the Estrada index [17,[23][24][25]30], the effect of a ring detected differences that certainly contribute to the observed fine variations in the predictive potential of the Estrada index and the resolvent energy of a graph.…”

“…In addition, this topological descriptor exhibited good performance in modeling physico-chemical properties, such as boiling point, heat of formation, and logP of hydrocarbons [24]. Lately, several articles have appeared in which the comparative analysis of the abovementioned topological indices has been exhibited [13,17,[23][24][25]. A similar type of analysis is performed here, aiming to investigate the influence of a ring in a molecule on the values of the eigenvalue-based topological indices.…”

“…was introduced recently [22]. Despite its juvenility, this index has attracted the attention of scientists thanks to its specific features and a noticeable predictive potential [13,17,[23][24][25][26][27][28][29]. For example, it has been shown that discriminating power of resolvent energy outperforms such feature of graph energy and Estrada index [30].…”