Investigation of Commuting Graphs for Elements of Order 3 in Certain Leech Lattice Groups

  • Duha Abbas Azeez Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
  • Ali Abd Aubad Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Keywords: Sporadic groups, commuting graph, diameter, cliques

Abstract

      Assume that G is a finite group and X is a subset of G. The commuting graph is denoted by С(G,X) and has a set of vertices X with two distinct vertices x, y Î X, being connected together on the condition of xy = yx. In this paper, we investigate the structure of Ϲ(G,X) when G is a particular type of Leech lattice groups, namely Higman–Sims group HS and Janko group J2, along with  X as a G-conjugacy class of elements of order 3. We will pay particular attention to analyze the discs’ structure and determinate the diameters, girths, and clique number for these graphs.

Published
2021-08-31
How to Cite
Azeez, D. A., & Aubad, A. A. (2021). Investigation of Commuting Graphs for Elements of Order 3 in Certain Leech Lattice Groups. Iraqi Journal of Science, 62(8), 2640-2652. https://doi.org/10.24996/ijs.2021.62.8.16
Section
Mathematics