Abstract
In chemical graph theory, graph entropy is an essential parameter. It measures chemical graphs and complicated networks. In discrete mathematics, biology, and chemistry, graph entropy measures have specialized chemical uses. The purpose of this paper is to discuss graph entropies and the structure of Titanium dioxide (TiO2). We developed a new idea of computing entropies of titanium dioxide based on the degree of end vertices. Moreover, we have computed graph entropy indices for real systems, and made correlations with thermodynamic quantities like heat of formation and (thermodynamic) entropy. Also, curves have been fitted between entropy indices and thermodynamics properties (entropy, enthalpy) rational method using MATLAB.