For a commutative ring R with unity (\(1\ne 0\)), the zero-divisor graph of R is a simple graph with vertices as elements of \(Z(R)^{*}=Z(R)\setminus \{ 0 \}\), where Z(R) is the set of zero-divisors of R and two distinct vertices are adjacent whenever their product is zero. An algorithm is presented to create a zero-divisor graph for the ring of Gaussian integers modulo \(2^{n}\) for \(n\ge 1\). The zero-divisor graph \(\Gamma (\mathbb {Z}_{2^{n}}[i])\) can be expressed as a generalized join graph \(G[G_{1}, \dots , G_{j}]\), where \(G_{i}\) is either a complete graph (including loops) or its complement and G is the compressed zero-divisor graph of \(\mathbb {Z}_{2^{2n}}\). Next, we show that the number of isomorphisms between the zero-divisor graphs for the ring of Gaussian integers modulo \(2^{n}\) and the ring of integers modulo \(2^{2n}\) is equal to \(\prod _{j=1}^{2(n-1)}2^{j}!\).

对于交换环- [R具有单位（\（1 \ NE 0 \） ），的零除数图表- [R是一个简单的图形与顶点作为元素\（Z（R）^ {*} = Z（R）\ setminus \ {0 \} \） ，其中ž（[R ）是该组的零除数ř和两个不同的顶点相邻每当他们的产品是零。提出的算法来创建高斯整数环零除数图形模\（2 ^ {N} \）为\（N \ GE 1 \） 。零因数图\（\ Gamma（\ mathbb {Z} _ {2 ^ {n}} [i]）\）可以表示为广义联接图\（G [G_ {1}，\ dots，G_ {j}] \），其中\（G_ {i} \）是完整图（包括循环）或其补码，G是\（\ mathbb {Z} _ {2 ^ {2n}} \）的压缩零因子图。接下来，我们证明高斯整数模\（2 ^ {n} \）的环和整数模\（2 ^ {2n} \）的零环的零除图之间的同构数等于\ （\ prod _ {j = 1} ^ {2（n-1）} 2 ^ {j}！\）。