Assume that R is a commutative ring with identity. In this thesis the zero-divisor graph of a commutative reduced ring R is studied. It is associated the ring properties of R , the graph properties of the zero-divisor graph and the topological properties of Spec ( R ). Then all graphs on 6,7,…,14 vertices which can be realized as the zero divisor graphs of a commutative rings with 1, and the list of all rings (up to isomorphism) which produce these graphs, are given.