Zero divisor graphs of semigroups

Let S be a commutative semigroup. If a and b in S and b is nonzero element then we call a is a zero divisor of S. The set of all zero divisors of S denoted by Z(S). Let Z*(S)=Z(S)\{0} and let E={(x,y): x and y in Z*(S) and x.y=0 } . If we define a graph which vertices are Z*(S) and which undirected edges are ordered pair of E , then there is a undirected graph and we call that graph is zero divisor graph of S. Let X be a nonempty and finite set and let SLx be the set consisting of all subsets of X except the empty set. Then SLx is finite free semilattice with operation of set union , we call it free semilattice on X . If X has n elements then we use SLx instead of SLn . In this study, we have researched basic properties of zero divisor graph of SLn . Moreover we have researched some properties of tensor product, lexicographic product and cartesian product of this graphs.