On Characterization of Topological Properties for Cubic Zirconia Network

Abstract

The utilization of graph theory in multiple branches of research has been vastly enhanced, particularly in the domain of chemical graph theory. Over the past few years, numerous researchers have been able to pursue a variety of novel avenues. A chemical graph is a named graph where the edges reflect chemical bonds between atoms and the vertices reflect the atoms of a compound. The investigation of topological indices is crucial for determining numerous physical and chemical characteristics of the under investigation molecular structures. 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 Cubic Zirconia Network (𝑍𝑟𝑂2). Afterwards, we found the physical measures like heat of formation of Cubic Zirconia Network (𝑍𝑟𝑂2). 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 Cubic Zirconia Network (𝑍𝑟𝑂2).