ZAGREB INDICES AND THE THERMAL BEHAVIOR OF STEROIDS: A QUANTITATIVE GRAPH-BASED STUDY

Abstract

In mathematical chemistry, graph theory provides a systematic and quantitative framework for understanding the relationship between molecular structure and the physicochemical properties of compounds. This study investigates the correlation between the first and second Zagreb indices and the melting points of a group of steroid compounds, bioactive molecules with significant pharmacological relevance. Ten steroid compounds were selected based on the availability of melting point data, and their chemical structures were modeled as molecular graphs. The Zagreb index values were calculated by analyzing the degrees of the vertices in each graph. Pearson correlation analysis and linear regression were employed to examine the relationship. The regression model for the first Zagreb index yielded an intercept of 245.77 with a coefficient of -0.1741 (p = 0.317), while the second Zagreb index produced an intercept of 224.92 with a coefficient of -0.091 (p = 0.495). Both analyses indicate weak and statistically insignificant negative correlations between Zagreb indices and melting points. These findings indicate that the Zagreb indices, in their current form, are insufficient to accurately capture variations in the melting points of steroid-based medicinal compounds. Nevertheless, this study underscores the potential of graph-based modeling in pharmaceutical chemistry.