M. Badie - Department of Mathematics, Jundi-Shapur University of Technology, P.O. Box ۶۴۶۱۵/۳۳۴, Dezful, Iran.

In this article the annihilating-ideal graph of the ring C(X) is studied. We have tried to associate the graph properties of AG(X), the ring properties of C(X) and the topological properties of X. It is shown that X has an isolated point if and only if R is a direct summand of C(X) and this happens if and only if AG(X) is not triangulated. Radius, girth, dominating number and clique number of the AG(X) are investigated. It is proved that c(X) <= dt(AG(X)) ,= w(X) and wAG(X) = χAG(X) = c(X).

Rings of real-valued continuous functions, Annihilating-ideal graph, Clique number, Chromatic number, Cellularity