on zero-divisor graphs of quotient rings and complemented zero-divisor graphs

for an arbitrary ring $r$, the zero-divisor graph of $r$, denoted by $gamma (r)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $r$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. it is well-known that for any commutative ring $r$, $gamma (r) cong gamma (t(r))$ where $t(r)$ is the (total) quotient ring of $r$. in this paper we extend this fact for certain noncommutative rings, for example, reduced rings, right (left) self-injective rings and one-sided artinian rings. the necessary and sufficient conditions for two reduced right goldie rings to have isomorphic zero-divisor graphs is given. also, we extend some known results about the zero-divisor graphs from the commutative to noncommutative setting: in particular, complemented and uniquely complemented graphs.