Journal of the
Korean Mathematical Society JKMS

The zero-divisor graph of a noncommutative ring $R$, denoted by $\Gamma(R)$, is a graph whose vertices are nonzero zero-divisors of $R$, and there is a directed edge from a vertex $x$ to a distinct vertex $y$ if and only if $xy=0$. Let $R=M_{2}(F_q)$ be the $2\times 2$ matrix ring over a finite field $F_q$. In this article, we investigate the automorphism group of $\Gamma(R)$.

Keywords: automorphism, zero-divisor graph, noncommutative ring, matrix ring

MSC numbers: 05C20, 05C60