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The zero-divisor graph of a ring $R$ is defined as the directed
graph $\Gamma(R)$ that its vertices are all non-zero zero-divisors
of $R$ in which for any two distinct vertices $x$ and $y$, $x
\rightarrow y$ is an edge if and only if $xy = 0$. Recently, it
has been shown that for any finite ring $R, \Gamma(R)$ has an even
number of edges. Here we give a simple proof for this result. In
this paper we investigate some properties of zero-divisor graphs
of matrix rings and group rings. Among other results, we prove
that for any two finite commutative rings $R,S$ with identity and
$n,m\geqslant 2$, if $\Gamma (M_{n}(R))\simeq \Gamma(M_{m}(S))$,
then $n = m$, $|R| = |S|$, and $\Gamma(R) \simeq \Gamma(S)$
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