Characterization of the symmetric group by its non-commuting graph
نویسندگان
1 University of Tehran
2 K. N. Toosi University of Technology
doi
10.22108/ijgt.2013.1920چکیده
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.
