Zero-divisor graph of C(X)

In this article the zero-divisor graph Gamma(C(X)) of the ring C(X) is studied. We associate 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.