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In this paper the zero-divisor graph $\Gamma(R)$ of a commutative
reduced ring $R$ is studied. We associate the ring properties of
$R$, the graph properties of $\Gamma(R)$ and the topological
properties of Spec$(R)$. Cycles in $\Gamma(R)$ are investigated
and an algebraic and a topological characterization is given for
the graph $\Gamma(R)$ to be triangulated or hypertriangulated. We
show that the clique number of $\Gamma(R)$, the cellularity of
Spec$(R)$ and the Goldie dimension of $R$ coincide. We prove that
when $R$ has the annihilator condition and $2 \notin Z(R);
\Gamma(R)$ is complemented if and only if Min$(R)$ is compact. In
a semiprimitive Gelfand ring, it turns out that the dominating
number of $\Gamma(R)$ is between the density and the weight of
Spec$(R)$. We show that $\Gamma(R)$ is not triangulated and the
set of centers of $\Gamma(R)$ is a dominating set if and only if
the set of isolated points of Spec$(R)$ is dense in Spec$(R)$.
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