Scientific interest in Titanium dioxide has increased due to its wide range of applications across various industries. Chemical design and development involve significant expense, time, and difficulties. Additionally, concerns about toxicity frequently make many chemicals unsuitable for testing, requiring continuous research endeavors to identify new substances without relying on expensive laboratory experiments. One of these methods involves using topological indices (TI), which are employed in predicting molecular properties and features. This study utilizes quantitative structure-property relationship (QSPR) analysis, employing innovative grade-based molecular descriptors and regression models for prediction. In this article, we use the M-polynomials (M-P) associated with the molecular and linear graph of Titanium dioxide nanotubes (TDN) to compute four derivatives of Rivan’s index. Additionally, theorems pertaining to this field are formulated. Then, the precise mass properties of fifteen organic compounds of titanium dioxide were randomly selected and analyzed. After that, linear regression models have been used to correlate composite properties with specific indicators. The findings validate the effectiveness of the chosen topological indices. Additionally, we computed these results using MATLAB coding on the M-polynomial.