The zero-divisor graph of a commutative ring without identity

Abstract

Let R be a commutative ring. The zero-divisor graph of R is the

(simple) graph 􀀀(R) with vertices the nonzero zero-divisors of R, and two

distinct vertices x and y are adjacent if and only if xy = 0. In this article, we

investigate 􀀀(R) when R does not have an identity, and we determine all such

zero-divisor graphs with 14 or fewer vertices.

Keywords

• Zero-divisor graph,commutative ring without identity

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