topological properties of commuting graphs over semi-dihedral groups

‎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.‎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. ‎