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The orbit graph of finite non-Abelian groups

Omer, Sanaa Mohamed Saleh and Sarmin, Nor Haniza and Erfanian, Ahmad (2015) The orbit graph of finite non-Abelian groups. Intertiol Jourl Of Pure And Applied Mathematics, 102 (4). pp. 747-755. ISSN 1311-8080

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Official URL: http://dx.doi.org/10.12732/ijpam.v102i4.12

Abstract

Let G be a finite non-abelian group and let Ω be a set of elements of G. Let A be the set of commuting elements in Ω, i.e A = {v ∈ Ω : vg = gv, g ∈ G}. In this paper, we extend the work on conjugate graph by defining a new graph called the orbit graph, denoted as ΓGΩ. The vertices of ΓGΩ are non central elements in Ω but not in A in which two vertices of ΓGΩ are adjacent if they are conjugate. Some graph properties are provided. Besides, the orbit graph of dihedral groups and quaternion groups is determined.

Item Type:Article
Uncontrolled Keywords:commutativity degree, conjugate graph, graph theory, group action
Subjects:A General Works
Divisions:Science
ID Code:58975
Deposited By: Haliza Zainal
Deposited On:04 Dec 2016 12:07
Last Modified:01 Feb 2017 09:31

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