The orbit graph of finite non-Abelian groups
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 cen...
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my.utm.589752021-12-07T03:04:41Z http://eprints.utm.my/id/eprint/58975/ The orbit graph of finite non-Abelian groups Omer, Sanaa Mohamed Saleh Sarmin, Nor Haniza Erfanian, Ahmad QA Mathematics 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. Academic Press 2015 Article PeerReviewed Omer, Sanaa Mohamed Saleh and Sarmin, Nor Haniza and Erfanian, Ahmad (2015) The orbit graph of finite non-Abelian groups. Intertional Journal Of Pure And Applied Mathematics, 102 (4). pp. 747-755. ISSN 1311-8080 http://dx.doi.org/10.12732/ijpam.v102i4.12 DOI:10.12732/ijpam.v102i4.12 |
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QA Mathematics Omer, Sanaa Mohamed Saleh Sarmin, Nor Haniza Erfanian, Ahmad The orbit graph of finite non-Abelian groups |
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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. |
| format |
Article |
| author |
Omer, Sanaa Mohamed Saleh Sarmin, Nor Haniza Erfanian, Ahmad |
| author_facet |
Omer, Sanaa Mohamed Saleh Sarmin, Nor Haniza Erfanian, Ahmad |
| author_sort |
Omer, Sanaa Mohamed Saleh |
| title |
The orbit graph of finite non-Abelian groups |
| title_short |
The orbit graph of finite non-Abelian groups |
| title_full |
The orbit graph of finite non-Abelian groups |
| title_fullStr |
The orbit graph of finite non-Abelian groups |
| title_full_unstemmed |
The orbit graph of finite non-Abelian groups |
| title_sort |
orbit graph of finite non-abelian groups |
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Academic Press |
| publishDate |
2015 |
| url |
http://eprints.utm.my/id/eprint/58975/ http://dx.doi.org/10.12732/ijpam.v102i4.12 |
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