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In this article the zero-divisor graph $\Gamma(C(X))$ of
the ring $C(X)$ is studied. We have associated the ring properties
of $C(X)$, the graph properties of $\Gamma(C(X))$ and the
topological properties of $X$. Cycles in $\Gamma(C(X))$ are
investigated and an algebraic and a topological characterization
is given for the graph $\Gamma(C(X))$ to be triangulated or
hypertriangulated. We have shown that the clique number of
$\Gamma(C(X))$, the cellularity of $X$ and the Goldie dimension of
$C(X)$ coincide. It turns out that the dominating number of
$\Gamma(C(X))$ is between the density and the weight of $X$.
Finally we have shown that $\Gamma(C(X))$ is not triangulated and
the set of centers of $\Gamma(C(X))$ is a dominating set if and
only if the set of isolated points of $X$ is dense in $X$ if and
only if the Socle of $C(X)$ is an essential ideal.
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