摘要
Let R be a commutative ring and Γ(R)be its zero-divisor graph.We completely determine the structure of all finite commutative rings whose zero-divisor graphs have clique number one,two,or three.Furthermore,if R■R1×R2×…×Rn(each Ri is local for i=1,2,3,...,n),we also give algebraic characterizations of the ring R when the clique number of Γ(R)is four.
基金
This research was supported by the National Natural Science Foundation of China(No.11801356,No.11401368,No.11971338)
by the Natural Science Foundation of Shanghai(No.19ZR1424100).
