On the Cozero-Divisor Graphs of Commutative Rings and Their Complements
نویسندگان
چکیده
Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by Γ′(R), is a graph with vertices in W ∗(R), which is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b in W ∗(R) are adjacent if and only if a / ∈ bR and b / ∈ aR. In this paper, we characterize all commutative rings whose cozero-divisor graphs are forest, star, double-star or unicyclic. 2010 Mathematics Subject Classification: 05C69, 05C75, 13A15
منابع مشابه
On the Cozero-Divisor Graphs of Commutative Rings
Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by , is a graph with vertices in R W R , which is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b in are adjacent if and only if and W R a bR b aR . In this paper, we investigate some combinatorial properties of the cozero-divisor graphs ...
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