Mazhar HussainCIIT/SP20-RMT-004/LHRDr. Sana JavedLHR TP 76232026-05-062021https://repository.cuilahore.edu.pk/123456789/3870In terms of graph theory, a molecular graph or chemical graph is a representation of the structural formula of a chemical compound. A chemical graph is a labeled graph in which the vertices represent the atoms of a compound and the edges represent chemical bonds between two atoms. In this thesis, we computed various connectivity indices based on degrees of vertices of chemical graph of Iron(III) Oxide (𝐹𝑒2𝑂3) and Titanium Dioxide (𝑇𝑖𝑂2) including general Randic, ABC, GA and Zagreb indices etc. Afterwards, we found the physical measures like entropy and heat of formation of Iron(III) Oxide (𝐹𝑒2𝑂3) and Titanium Dioxide (𝑇𝑖𝑂2). Then, we fitted curves between different indices and the thermodynamical properties namely heat of formation and entropy. Curve fitting was done in MATLAB through different methods based on linearity and non-linearity. The performance of the method was tested using mean squared error (MSE), the sum of squared errors (SSE) or R2. Further, we gave graphical representations of these indices. These mathematical frameworks might provide a way to study the thermodynamical properties of the chemical structure Iron(III) Oxide (𝐹𝑒2𝑂3) and Titanium Dioxide (𝑇𝑖𝑂2) at intense level which will assist to comprehend the relationship between system dimension and these measures. This thesis is divided into five chapters. Chapter 1 contains basic definitions, notions and terminologies related to this thesis. Chapter 2 provides a review of literature about our work. The main results are given in chapter 3. Chapter 4 contains a brief discussion about the work while chapter 5 consist of the references used in this thesis.enDepartment of MathematicsSP20Mathematicschemical graph theorytopological indicesgraphical descriptorsDr. Sana JavedThesis