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Paper   IPM / M / 7784
School of Mathematics
  Title:   Zero-divisor graph of C(X)
1.  F. Azarpanah
2.  M. Motamedi
  Status:   Published
  Journal: Acta Math. Hungar.
  Vol.:  108
  Year:  2005
  Pages:   25-36
  Supported by:  IPM
In this article the zero-divisor 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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