  The zero-divisor graph $\Gamma(R)$ of an associative ring $R$ is the graph
whose vertices are all nonzero zero-divisors (one-sided and two-sided) of $R$,
and two distinct vertices $x$ and $y$ are joined by an edge iff either $xy=0$
or $yx=0$.
  In the present paper, we give a full description of ring varieties where
every finite ring is uniquely determined by its zero-divisor graph.
