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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| Format: | Article |
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Academic Press
2015
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| Summary: | 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. |
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