%0 Journal Article
%T Characterization of the symmetric group by its non-commuting graph
%A M.R. Darafsheh
%A Pedram Yousefzadeh
%J International Journal of Group Theory
%D 2013
%I University of Isfahan
%X 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 'll prove that if $G$ is a finite group with $nabla(G)congnabla(BS_{n})$, then $G cong BS_{n}$, where $BS_{n}$ is the symmetric group of degree $n$, where $n$ is a natural number.
%K non-commuting graph
%K symmetric group
%K finite groups
%U http://www.theoryofgroups.ir/?_action=showPDF&article=1920&_ob=4d6dd70c53a2f3584898f92c49fe8cf5&fileName=full_text.pdf