University of Isfahan International Journal of Group Theory 2251-7650 2 2 2013 06 01 Characterization of the symmetric group by its non-commuting graph 47 72 1920 10.22108/ijgt.2013.1920 EN Mohammad Reza Darafsheh University of Tehran Pedram Yousefzadeh K. N. Toosi University of Technology Journal Article 2012 08 30 ‎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. https://ijgt.ui.ac.ir/article_1920_4d6dd70c53a2f3584898f92c49fe8cf5.pdf