Darafsheh, M., Yousefzadeh, P. (2013). Characterization of the symmetric group by its non-commuting graph. International Journal of Group Theory, 2(2), 47-72.

Mohammad Reza Darafsheh; Pedram Yousefzadeh. "Characterization of the symmetric group by its non-commuting graph". International Journal of Group Theory, 2, 2, 2013, 47-72.

Darafsheh, M., Yousefzadeh, P. (2013). 'Characterization of the symmetric group by its non-commuting graph', International Journal of Group Theory, 2(2), pp. 47-72.

Darafsheh, M., Yousefzadeh, P. Characterization of the symmetric group by its non-commuting graph. International Journal of Group Theory, 2013; 2(2): 47-72.

Characterization of the symmetric group by its non-commuting graph

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.