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The zero-divisor graph $\Gamma(R)$ of an associative ring $R$ is the graphwhose 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 whereevery finite ring is uniquely determined by its zero-divisor graph.

Full Descripion of ring varieties whose finite rings are uniquely determined by their zero-divisor graphs