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Abstract
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Let Zd(R) denotes the set of zero divisors of a ring R. Define an equivalence
relation ~ on Zd(R) as follows: x ~ y if and only if ann(x) = ann(y). The
graph \Gamma_E(R) is a graph associated to R whose vertices are the classes of
elements in Zd(R)^* = Zd(R)\{0}, and two distinct classes [x] and [y] are
joined by an edge if and only if xy = 0. In this paper we give a complete
classification of finite graphs which are the compressed zero divisor graphs
of reduced rings by using Goldie’s theorem.
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