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 $\mathrm{G}$. Let $\mathrm{X}=t^{\mathrm{G}}$ be a conjugacy class of $t$ in $\mathrm{G}$. The A4-graph, represented as $A_{4}(\mathrm{G}, \mathrm{X})$, is a simple graph has $\mathrm{X}$ as a vertex set and two vertices $x, y \in \mathrm{X}$, joined by edge whenever $\mathrm{x} \neq \mathrm{y}$ and $x y^{-1}=y x^{-1}$. In this paper, we investigate the discs structure and determine the clique number, girth and diameter of $A_{4}(\mathrm{G}, \mathrm{X})$ when $\mathrm{G}$ is isomorphic to one of the untwisted groups $\mathrm{G}_{2}(2)^{\prime}, \mathrm{G}_{2}(3)$ or $\mathrm{G}_{2}(4)$.

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