International Journal of Nonlinear Analysis and Applications

The disc structures of A4-graph for particular untwisted groups

Document Type : Research Paper

Authors

1 Technical Instructors Training Institute, Middle Technical University, Baghdad, Iraq

2 Technical Engineering College, Middle Technical University, Baghdad, Iraq

3 College of Physical Education and Sports Science, University of Baghdad, Baghdad, Iraq

4 Middle Technical University, Technical Instructors Training Institute, Iraq

Abstract

Let t be an elements of order 3 in a finite simple group G. Let X=tG be a conjugacy class of t in G. The A4-graph, represented as A4(G,X), is a simple graph has X as a vertex set and two vertices x,y∈X, joined by edge whenever x≠y and xy−1=yx−1. In this paper, we investigate the discs structure and determine the clique number, girth and diameter of A4(G,X) when G is isomorphic to one of the untwisted groups G2(2)′,G2(3) or G2(4).

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 2
July 2022
Pages 527-533
  • Receive Date: 16 January 2022
  • Revise Date: 28 February 2022
  • Accept Date: 30 March 2022