University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 16 2 2025 06 01 Topological Properties of Commuting Graphs over Semi-Dihedral Groups 109 126 114905 10.22052/ijmc.2024.254494.1840 EN Fawad Ali College of Mathematical Sciences and Statistics‎, ‎Baise University‎, ‎Guangxi‎, ‎Baise 533000‎, ‎China\\ Department of Mathematics‎, ‎COMSATS University Islamabad‎, ‎Park Road‎, ‎Tarlai Kalan‎, ‎Islamabad 455505 Pakistan Kumail Raza Institute of Numerical Sciences‎, ‎Kohat University of Science & Technology‎, ‎Kohat 26000‎, ‎KPK‎, ‎Pakistan Tanzeela Rubab Institute of Numerical Sciences‎, ‎Kohat University of Science & Technology‎, ‎Kohat 26000‎, ‎KPK‎, ‎Pakistan Journal Article 2024 03 01 ‎The algebraic value of a chemical composition plays a crucial role in determining its physical properties‎, ‎chemical reactivity‎, ‎and biological activity‎. Algebraic graph theory investigates the connection between abstract algebra and graph theory‎. Focusing on the commuting graphs of semi-dihedral groups‎, ‎we examine their various topological properties‎.<br />‎Furthermore‎, ‎we provide a detailed exploration of key topological graph indices‎, ‎including the general Randi\'{c} index‎, ‎the Wiener index‎, ‎the atom-bond connectivity index (and its fourth variation)‎, ‎the Schultz molecular topological index‎, ‎the geometric-arithmetic index‎, ‎the harmonic index‎, ‎and the Harary index‎. This research reveals the structural as well as mathematical features of these graphs‎, ‎providing valuable insights into their possible applications‎. ‎ Distance property Chemical graph Molecular structure Commuting graph finite group https://ijmc.kashanu.ac.ir/article_114905_36cf19ed65cfcb8f1cf9d26bbea1dfcc.pdf