Shahrood University of TechnologyJournal of Algebraic Systems2345-51289220220101ANNIHILATING-IDEAL GRAPH OF C(X)203217219310.22044/jas.2021.10008.1496ENM. BadieDepartment of Mathematics, Jundi-Shapur University of Technology, P.O. Box
64615/334, Dezful, Iran.Journal Article20200824In 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