On exploring the statistical behavior of Sombor and Revan indices in chemical networks

This research explores the statistical behavior of Sombor and Revan indices of Quadrilateral Carbon Nanocones to enable predictive modeling in chemical network analysis. Using Euclidean geometry and graph-theoretic approaches, a number of novel indices, namely Reduced Sombor, Increased Sombor, Reverse Sombor, and Revan indices, are introduced and comparatively analyzed. Quadratic regression models emerged as the best predictors, offering precise correlations between these indices and the structural features of nanocones. Comprehensive statistical validation by measures such as Mean Squared Error, Root Mean Squared Error, Mean Absolute Error, Mean Absolute Percentage Error, and Mean Percentage Error ensures the stability of the proposed models. The findings attest to the usefulness of Sombor and Revan indices for the description of nanostructures, providing useful insights into their stability, reactivity, and electronic properties. Furthermore, the study presents explicit formulas for the indices, revealing the effectiveness of these descriptors in modeling carbon-based nanomaterials. The findings show promise for the application of these indices in the design and analysis of nanostructures in materials science and nanotechnology.