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-based distance 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.