# The Zero-Divisor Graph of a Commutative Ring☆

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### Cites background from "The Zero-Divisor Graph of a Commuta..."

...In [3], Anderson and Livingston introduced the zero-divisor graph of R, denoted by Γ (R), as the (undirected) graph with vertices Z(R)∗ = Z(R)\{0}, the set of nonzero zero-divisors of R, and for distinct x, y ∈ Z(R)∗, the vertices x and y are adjacent if and only if xy = 0....

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### Cites background from "The Zero-Divisor Graph of a Commuta..."

...on studying the interplay between graph-theoretic properties of (R) and ring-theoretic properties of R are from [4]....

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##### References

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### "The Zero-Divisor Graph of a Commuta..." refers background in this paper

...This concept is due to Beck [16], who let all the elements of R be vertices and was mainly interested in colorings (also see [2])....

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...The idea of a zero-divisor graph of a commutative ring was introduced w xby I. Beck in 2 , where he was mainly interested in colorings....

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