Generalized Commuting Graph of Dihedral, Semi-dihedral and Quasi-dihedral Groups


  • Mustafa Anis El-Sanfaz Department of Mathematics, Statistics and Physics, College of Arts, Qatar University, Doha, Qatar
  • Nor Haniza Sarmin Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
  • Siti Norziahidayu Amzee Zamri UniSZA Science and Medicine Foundation Centre, Universiti Sultan Zainal Abidin, Gong Badak Campus, 21300 Kuala Nerus, Terengganu



graph theory, commuting graph, dihedral groups, semi-dihedral groups, quasi-dihedral groups


Commuting graphs are characterized by vertices that are non-central elements of a group where two vertices are adjacent when they commute. In this paper, the concept of commuting graph is extended by defining the generalized commuting graph. Furthermore, the generalized commuting graph of the dihedral groups, the quasi-dihedral groups and the semi-dihedral groups are presented and discussed. The graph properties including chromatic and clique numbers are also explored.


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