The non-commuting graph $\nabla(G)$ of a non-abelian group $G$ is defined as follows: its vertex set is $G-Z(G)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. In this paper we prove that if $G$ is a finite group with $\nabla(G) \cong \nabla(BS_n)$, then $G \cong BS_n$, where $BS_n$ is the symmetric group of degree $n$, where $n$ is a natural number.
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Darafsheh, M. R. and Yousefzadeh, P. (2013). Characterization of the symmetric group by its non-commuting graph. International Journal of Group Theory, 2(2), 47-72. doi: 10.22108/ijgt.2013.1920
MLA
Darafsheh, M. R. , and Yousefzadeh, P. . "Characterization of the symmetric group by its non-commuting graph", International Journal of Group Theory, 2, 2, 2013, 47-72. doi: 10.22108/ijgt.2013.1920
HARVARD
Darafsheh, M. R., Yousefzadeh, P. (2013). 'Characterization of the symmetric group by its non-commuting graph', International Journal of Group Theory, 2(2), pp. 47-72. doi: 10.22108/ijgt.2013.1920
CHICAGO
M. R. Darafsheh and P. Yousefzadeh, "Characterization of the symmetric group by its non-commuting graph," International Journal of Group Theory, 2 2 (2013): 47-72, doi: 10.22108/ijgt.2013.1920
VANCOUVER
Darafsheh, M. R., Yousefzadeh, P. Characterization of the symmetric group by its non-commuting graph. International Journal of Group Theory, 2013; 2(2): 47-72. doi: 10.22108/ijgt.2013.1920