ANNIHILATING-IDEAL GRAPH OF C(X)

The annihilating-ideal graph of the ring C(X) is studied. It is 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 AG(X) are investigated. It is proved that c(X) ⩽ dt(AG(X)) ⩽ w(X) and !AG(X) = AG(X) = c(X).