Geometric-Quadratic and Quadratic-Geometric Indices-based Entropy Measures of Silicon Carbide Networks

In chemical graph theory, topological indices are numerical quantities associated with the structure of molecular compounds. These indices are utilized in the construction of quantitative structure-property relationships (QSPR) and quantitative structure-activity relationships (QSAR) analysis and quantify the different features of the molecular topology. M-polynomial gives a handy method for managing complex computations involving various indices and offers a consistent methodology to derive multiple degree-based topological indices. Graph entropy measures are employed to measure the structural information content, disorder and complexity of a graph. In this article, we examine the geometric-quadratic (GQ) and quadratic-geometric (QG) indices for silicon carbide networks, namely Si2C3-I[p,q]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {Si}_{2}\text {C}_{3} \textit{-I}[p,q]$$\end{document}, Si2C3-II[p,q]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {Si}_{2}\text {C}_{3} \textit{-II}[p,q]$$\end{document} and Si2C3-III[p,q]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {Si}_{2}\text {C}_{3} \textit{-III}[p,q]$$\end{document} with the help of their respective M-polynomials. Next, we propose the idea of the GQ-QG indices-based entropy measure and compute their expressions for the above-said networks. Furthermore, the graphical representation and numerical computation of the GQ-QG indices and associated entropy measures are performed to assess their behavior. These indices and entropy measures may be helpful in predicting the physico-chemical properties and understanding the structural behavior of the considered silicon carbide networks.