Characterization of the symmetric group by its non-commuting graph
Author(s):
Abstract:
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.
Keywords:
Language:
English
Published:
International Journal of Group Theory, Volume:2 Issue: 2, Jun 2013
Pages:
47 to 72
https://www.magiran.com/p1091370