TY - JOUR
ID - 2193
TI - ANNIHILATING-IDEAL GRAPH OF C(X)
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Badie, M.
AD - Department of Mathematics, Jundi-Shapur University of Technology, P.O. Box
64615/334, Dezful, Iran.
Y1 - 2022
PY - 2022
VL - 9
IS - 2
SP - 203
EP - 217
KW - Rings of real-valued continuous functions
KW - Annihilating-ideal graph
KW - Clique number
KW - Chromatic number
KW - Cellularity
DO - 10.22044/jas.2021.10008.1496
N2 - 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).
UR - https://jas.shahroodut.ac.ir/article_2193.html
L1 - https://jas.shahroodut.ac.ir/article_2193_db1062600571017f02164e5aab615fcb.pdf
ER -