Bulletin of the
Korean Mathematical Society BKMS

Let $G$ be a finite non-abelian group. We define the non-commuting graph $\nabla(G)$ of $G$ as follows: the vertex set of $\nabla(G)$ is $G- Z (G)$ and two vertices $x$ and $y$ are adjacent if and only if $xy\neq yx$. In this paper we prove that if $G$ is a finite group with $\nabla(G)\cong\nabla(\mathbb{A}_{22})$, then $G \cong \mathbb{A}_{22}$, where $\mathbb{A}_{22}$ is the alternating group of degree 22.

Keywords: finite group, non-commuting graph, prime graph, alternating group

MSC numbers: 20D05, 20D06, 20D60