“School of Mathematics”
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Paper IPM / M / 7784  


Abstract:  
In this article the zerodivisor graph Γ(C(X)) of
the ring C(X) is studied. We have associated the ring properties
of C(X), the graph properties of Γ(C(X)) and the
topological properties of X. Cycles in Γ(C(X)) are
investigated and an algebraic and a topological characterization
is given for the graph Γ(C(X)) to be triangulated or
hypertriangulated. We have shown that the clique number of
Γ(C(X)), the cellularity of X and the Goldie dimension of
C(X) coincide. It turns out that the dominating number of
Γ(C(X)) is between the density and the weight of X.
Finally we have shown that Γ(C(X)) is not triangulated and
the set of centers of Γ(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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