In this paper, we provide efficient regression models for correlating the π‐electronic energies of carbon nanotubes and nanocones. First, a computational technique for determining distance‐based, eccentricity‐based, degree‐distance‐based, and degree‐based molecular descriptors is proposed. Then, the application of our technique has been explained for the family of fibonacenes. Importantly, we use the proposed computational technique to determine commonly occurring distance‐based molecular descriptors and generate regression models to determine their correlation with the π‐electronic energies of lower polycyclic aromatic hydrocarbons (PAHs). Unlike its reputation among chemical graph theorists and reticular chemists, the fourth version of the geometric–arithmetic index outperforms all the distance‐based descriptors having the correlation coefficient 0.999. This warrants further usage of the fourth geometric–arithmetic index in quantitative structure‐activity relationship models. To ensure the applicability of our proposed study, we use the proposed computational technique to compute analytically explicit expressions for certain distance‐based molecular descriptors for certain infinite families of carbon nanotubes and carbon nanocones. Our results assist in correlating the π‐electronic energies of underlying chemical structures of these nanotubes and nanocones.
Graph signal processing deals with signals whose domain, defined by a graph, is irregular. The total π-electron energy or simply the π-electronic energy, as calculated within the Hückel 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-baseddistance descriptors for measuring the π-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 π-electronic energy of these nanotubes and nanocones theoretically with higher accuracy and negligible error.INDEX TERMS Graph signal processing, Quantum chemistry, Chemical graph theory, Eigenvaluesbased topological descriptors, π-electronic energy, Benzenoid hydrocarbons, Carbon nanotubes, Carbon nanocones
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