The non-zero divisor graph for the ring of Gaussian integers

Let R be a ring. A non-zero divisor graph of R is defined as a graph where its vertices are the non-zero elements of R, and two vertices x and y are adjacent if the product of these two vertices is not equal to zero. In this study, the non- zero divisor graphs are constructed for the ring of Gaussian integers modulo 2n. The non-zero divisors for the ring need to be found first. Then, the non-zero divisor graph is constructed by using its definition. Two properties of the graph, known as the clique number and the chromatic number are obtained and this graph is found to be not perfect. The total perfect code of the graph is also found in this research.