Topological Properties of Commuting Graphs over Semi-Dihedral Groups

Document Type : Research Paper

Authors

1 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

2 Institute of Numerical Sciences‎, ‎Kohat University of Science & Technology‎, ‎Kohat 26000‎, ‎KPK‎, ‎Pakistan

10.22052/ijmc.2024.254494.1840

Abstract

‎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. ‎

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References

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Iranian Journal of Mathematical Chemistry
Volume 16, Issue 2
In Progress
June 2025
Pages 109-126

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