Comparative study between Nirmala and Sombor indices based on their applicability, degeneracy and smoothness

A topological index (or descriptor) is a numerical demonstration of a molecular graph associated with a chemical compound that directly correlates with its physical and chemical characteristics through quantitative structure–property relationship (QSPR) analysis. This article is concerned with the mathematical bounds and expressions of the Nirmala index for chemical graphs and its comparison with the Sombor index through QSPR analysis. More precisely, a comparative study between the Nirmala index and the Sombor index is presented using the linear, quadratic and multi-linear regression analysis over the physico-chemical properties of octane isomers to test the predictive potential of the index. Further, the degeneracy and smoothness (structure sensitivity and abruptness) are calibrated of the Nirmala and Sombor indices using the chemical isomers data sets such as octane, nonane and decane. Finally, the lower and upper bounds of the Nirmala index are investigated using the sets of chemical graphs and trees. Additionally, the expressions of the Nirmala index and its extremal values are also examined for different types of hexagonal systems. The obtained correlation values and p-values of both indices through multi-linear regression analysis are more significant, indicating the reliability and applicability of the findings. Therefore, these indices may be utilized to predict the properties of various chemical compounds and drugs in the QSPR studies.