This thesis order based on refrence [16] . Let R be a commutative ring with identity 1 \\ 0 . Let ZD(R) denote the set of zero-divisors of R including zero element , and let ZD(R)*=ZD(R)\\{0} . The zero-divisor graph of , denoted ?(R) , is the undirected graph whose vertices are labeled by the elements of ZD(R)* and is an edge in ?(R) between the vertices r and s if and only if rs = 0 . In this case , we say that r and s are adjacent . The set of vertices of ?(R) is V(?(R))= ZD(R)* and the set of edges of ?(R) is E(?(R))= { (r, s) | r, s ? ZD(R)*, rs=0}. The zero-divisor graph of a non-commutative ring R is a directed graph , which is denoted by (R). An element r ? R is a left zero-divisor if there exist 0 ? s ? R such that rs = 0 . In R the set of nonzero left zero-divisors is denoted (R)* . Likewise , an element r ? R is a right zero-divisor if there exists 0 ? s ? R such that sr = 0 . The set of nonzero right zero-divisors of R is denoted (R)* . The vertex set of R) is V(?((R)) = (R)* ? (R)* . The edges of (R) are directed; there is an edge from r to s , denoted r ? s , if and only if rs = 0 . In this case , we say that the edge is incident from r and incident to s .In this thesis , we study the zero-divisor graphs of upper triangular matrix rings over commutative rings with identity . Let R be a commutative ring with identity 1 ? 0 , and let R) denote the × n upper triangular matrix ring over R .