Abstract
Graph signal processing deals with signals whose domain, defined by a graph, is irregular. The total $\pi $ -electron energy or simply the $\pi $ -electronic energy, as calculated within the Huckel tight-binding molecular orbital approximation, is one of the important quantum-theoretical characteristic of conjugated molecules. In this paper, we propose an efficient computer-assisted computational method to determine eigenvalues-based distance descriptors for chemical compounds which are then used to learn to quantitative relationship between the activity/property and the structure (QSAR/QSPR) of compound. Comparisons with other similar methods show that our proposed method possesses less algorithmic and computational complexities and is more computationally diverse. The proposed method is used to determine predictive potential of eigenvalues-based distance descriptors for measuring the $\pi $ -electronic energy of benzenoid hydrocarbons. Importantly, we propose three new chemical matrices and, unexpectedly, results show that the spectral descriptors defined based on new chemical matrices outperform all the well-known descriptors in the literature. Specifically, our proposed second atom-bond connectivity Estrada index show the best correlation coefficient of 0.9997. Applications of our computational method to certain infinite families of carbon nanotubes and carbon nanocones are presented. The obtained results can potentially be used to determine the $\pi $ -electronic energy of these nanotubes and nanocones theoretically with higher accuracy and negligible error.
Highlights
Graph signal processing (GSP) [72] have been found potentially useful in devising diversified advanced solutions in many applications [29], [51], [57] and, has become an active area of research in recent years
We investigate the prediction potential of all commonly occurring distance-based spectral descriptors for determining the π-electronic energy of lower polycyclic aromatic hydrocarbons (PAHs)
Based on the spectrum-based indices for matrices defined in previous subsections, we investigate the chemical applicability of the Schultz spectral radius, energy and Estrada index
Summary
Graph signal processing (GSP) [72] have been found potentially useful in devising diversified advanced solutions in many applications [29], [51], [57] and, has become an active area of research in recent years. Motivation of this study comes from the seminal work of Gutman and Tošović [37] who tested the quality of valency-based descriptors for measuring the normal boiling point and the standard enthalpy of formation of acyclic chemical structures. Spectrum-based topological descriptors induce regression models with considerable efficiency for various physicochemical and quantum characteristics such as the π-electronic energy They are defined based on eigenvalues of certain chemical matrices. Hayat et al [45] determined the prediction power of all commonly occurring distance-based descriptors for determining the π-electronic energy of PAHs. the prediction potential of eigenvalues/spectrumbased topological descriptors such as the adjacency energy is significantly better than those of valency-based and distancebased topological descriptors. We compute the five best distance-based topological descriptors for certain infinite families of carbon nanotubes and carbon nanocones
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