On some properties of ring varieties, where isomorphic zero-divisor graphs of finite rings give isomorhic rings

Denote by $\Gamma(R)$ the zero-divisor graph of an associative ring $R$. In this paper, we study varieties of associative rings, where an isomorphism of $\Gamma(R)$ and $\Gamma(S)$ implies an isomorphism of the rings $R$ and $S$ for any finite rings $R$, $S$.