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The zero divisor graph of a commutative semigroup with zero is a graph whose vertices are the nonzero zero divisors of the semigroup, with two distinct vertices joined by an edge in case their product in the semigroup is zero. We continue the study of this construction and its extension to a simplicial complex.  2004 Elsevier Inc. All rights reserved. This article continues the study of the zero divisor graph of a commutative semigroup begun (implicitly) in [1,2] and in [4,5], though it is mostly self contained. Throughout S denotes a commutative semigroup with 0 whose operation is written multiplicatively. Associate to S a simple graph G whose vertices are the nonzero zero divisors of S with x = y connected by an edge in case xy = 0. Since the zero divisors of S form an ideal in S, we usually assume S consists of zero divisors. Observe though, that an ideal in a zero divisor semigroup may not consist of zero divisors. For example, If S = {0, x, y | x 2 = x, y 2 = y, xy = 0} then S consists of zero divisors but the ideal {0, x} does not. Recall the semigroup S is nilpotent in case for each x ∈ S there is a positive integer n with x n = 0. Every subsemigroup of a nilpotent semigroup consists of zero divisors. Moreover, in order that G be non empty, we usually assume S always contains at least one nonzero

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