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

Yu. N. Maltsev, E. V. Zhuravlev, A. S. Kuzmina

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 $x$ a…