International Journal of Pure and Applied Mathematics, Volume (102), No (4), Year (2015-12) , Pages (747-755)

Title : ( The Orbit Graph of Finite Non-Abelian Groups )

Authors: S. M. S. Omer , N. H. Sarmin , Ahmad Erfanian ,

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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 Γ G. The vertices of ΓΩ G are non central elements in Ω but not in A in which two vertices of Γ Ω G are adjacent if they are conjugate. Some graph properties are provided. Besides, the orbit graph of dihedral groups and quaternion groups is determined.

Keywords

, commutativity degree, graph theory, group action, conjugate
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@article{paperid:1055252,
author = {S. M. S. Omer and N. H. Sarmin and Erfanian, Ahmad},
title = {The Orbit Graph of Finite Non-Abelian Groups},
journal = {International Journal of Pure and Applied Mathematics},
year = {2015},
volume = {102},
number = {4},
month = {December},
issn = {1311-8080},
pages = {747--755},
numpages = {8},
keywords = {commutativity degree; graph theory; group action; conjugate graph},
}

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%0 Journal Article
%T The Orbit Graph of Finite Non-Abelian Groups
%A S. M. S. Omer
%A N. H. Sarmin
%A Erfanian, Ahmad
%J International Journal of Pure and Applied Mathematics
%@ 1311-8080
%D 2015

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