Exploring triangular prism networks TP(s) through the connection number approachExploring triangular prism networks...M. M. Hassan, X.-F. Pan

A triangular prism is a geometric object that has three rectangular sides and two triangular bases in three dimensions. It disperses light by separating various wavelengths and exposing the spectrum components of a beam, which is useful in physics and chemistry. The purpose of the TP-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$TP-$$\end{document}network in spectroscopy is to examine the unique emission or absorption spectra of various substances. Triangular prism networks are essential because they improve communication, transportation, and visualization technologies by providing realistic 3D representations, increasing traffic flow, and enabling effective signal transmission. The highly ordered and porous structure of the triangular prism network can be used to create photonic crystals and electronic devices with unique optical and electronic properties. In addition, the triangular prism network may be used to represent quantum states, conductivity, percolation, and network dynamics in physics. The main objective of this study is to compute the connection number-based Zagreb indices, which are used to assess the structural complexity of a triangular prism network. The calculated results are the ABCc-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ABCc-$$\end{document}index, GAc-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$GAc-$$\end{document}index, AZc-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$AZc-$$\end{document}index, Hc-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Hc-$$\end{document}index, ZC1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ZC_{1}$$\end{document}, ZC2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ZC_{2}$$\end{document}, and ZC1∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ZC_{1}^{*}$$\end{document}. The connection number derived using the vertex degree approach is used to meet the study’s purpose. The conclusion is preceded by a visual comparison of statistical data.