LetSbe a commutative semigroup with zero. LetZ(S) be the set of allzero-divisors ofS. We define the annihilator graph ofS, denoted byAN NG(S), asthe undirected graph whose set of vertices isZ(S)∗=Z(S)−{0}, and two distinctverticesxandyare adjacent if and only ifannS(xy)6=annS(x)∩annS(y). In thispaper, we study some basic properties ofAN NG(S) by means of Γ(S). We also showthat ifZ(S)6=S, thenAN NG(S) is a subgraph of Γ(S). Moreover, we investigatesome properties of the annihilator graphAN NG(S) related to minimal prime idealsofS. We also study some connections between the domination numbers of annihilatorgraphs and zero-divisor graphs.
