Shahrood University of Technology Journal of Algebraic Systems 2345-5128 9 2 2022 01 01 ANNIHILATING-IDEAL GRAPH OF C(X) 203 217 2193 10.22044/jas.2021.10008.1496 EN M. Badie Department of Mathematics, Jundi-Shapur University of Technology, P.O. Box 64615/334, Dezful, Iran. Journal Article 2020 08 24 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). https://jas.shahroodut.ac.ir/article_2193_db1062600571017f02164e5aab615fcb.pdf