Abstarct: In this thesis first, we recall the definitions and basic properties of zero-divisor graphs of commutative and noncommutative rings. Then we showed that Γ(R) and Γ(Q(R)) were isomorphic as graphs, and as a consequence it followed that these two graphs has the same diameter and girth. Also, We investigate the properties of (directed) zero-divisor graphs of matrix rings. Then we use these results to discuss the relation between the diameter of the zero-divisor graph of a commutative ring R and that of the matrix ring Mn(R). Also, we characterize when either diam(Γ(R)) ≤ 2 or gr(Γ(R)) ≥ 4. We then use these results to investigate the diameter and girth for the zero-divisor graphs of polynomial rings, power series rings, and idealizations. Fainally, we investigate the zero-divisor graph of triangular matrix rings over commutative rings.