Compressed Zero-Divisor Graphs

We define an equivalence relation on the set of zero-divisors to be that x is equivalent to y if the annihilators of x equal the annihilators of y.

A Compressed Zero-Divisor Graph, denoted Γ_E(R), is a graph where the vertices are the equivalence classes of the nonzero zero-divisors as defined above and two vertices are connected if and only if there product is zero.