On Statistical Analysis of Topological Indices for Titanium Diboride Network

Abstract

The use of graph theory to many fields of study has increased significantly, especially in the field of chemical graph theory. Many scholars have been able to explore a range of new directions in the last few years. A chemical graph is a named graph in which the atoms of a compound are represented at the vertices, and the edges represent chemical bonds between atoms. Determining various physical and chemical properties of the molecular structures under study requires an examination of topological indices. Firstly, we focused on degree based topological indices, namely Randic index, atom bond connectivity index, geometric arithmetic index, the first and the second Zagreb indices and co-indices, the first and the second multiple Zagreb indices and co-indices, hyper Zagreb index, forgotten index, augmented Zagreb index, Balaban index, redefined Zagreb type indices, of Titanium Diboride Network TiB2. Afterwards, we found the physical measures like heat of formation of Titanium Diboride Network TiB2. Then, we fitted curves between different indices and corresponding heat of formation. 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 thermo dynamical properties of the chemical structure Titanium Diboride Network TiB2. ix