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The zero-divisor graph of ring $R$ is the graph whose vertices consist of the non-zero zero-divisors of $R$ in which
two distinct vertices $a$ and $b$ are adjacent if and only if either $ab=0$ or $ba=0$. In this paper, we
investigate some properties of zero-divisor graphs of Boolean rings. Among other results, we prove that for any two
rings $R$ and $S$ with $\Gamma(R)\simeq \Gamma(S)$, if $R$ is Boolean and $|R|>4$, then $R\simeq S$.
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