A novel descriptor of molecular graphs and its implications in QSPR studies of antiviral drugs

Das et al [1] recently proposed a novel descriptor named as augmented Sombor index (ASO), and reported its chemical applicability in hydrocarbons. In present paper, the molecular trees and molecular unicyclic graphs of a fixed order possessing the extremum ASO values are characterized, and sharp bound on ASO corresponding to these extremal graphs are obtained. In addition, we extended the work presented in this current paper for chemical applicability of ASO index and examined the comparative analysis between ASO and some well-known degree-based topological indices named as reciprocal augmented Sombor index (RASO), atom-bond sum connectivity index (ABS) and atom-bond connectivity index (ABC), using 67 antiviral drug structures and obtained the robust and near-perfect correlation. Also we established the quantitative structure-property relationship (QSPR) analysis between the ASO and physicochemical properties (heavy atom count (HAC), molar refractivity (MR), topological surface area (TPSA), molecular weight (MW)) of antiviral drug structures. Throughtout this analysis, we used models such as linear regression, polynomial regression, ridge regression and lasso regression, consider ASO as the predictor variable (or source feature), and all other indices as the target (or response) variables in each model, Likewise, we used the ASO source feature and physicochemical properties as the target or response variables, and obtained highly predictive models. We obtained error metrics such as Mean Absolute Error(MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE) in regression analysis to quantify how close model's predicted values are to the actual observed values. We use these metrics together because they treat prediction errors differently, allowing us to accurately diagnose model accuracy and identify severe errors. We used statistical tools scatterplot matrix to multivariate exploratory data analysis and correlation matrix for summarizing data to identify relationships, used the matrix plot and show that the positive collinearity among all four Indices.