Annihilating-Ideal Graph of $C(X)$

Abstract

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