On zero-divisor graph of the ring of Gaussian integers modulo $2^n$

Abstract

For a commutative ring $R$, the zero-divisor graph of $R$ is a simple graph with the vertex set as the set of all zero-divisors of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if $xy = 0$. This article attempts to predict the structure of the zero-divisor graph of the ring of Gaussian integers modulo $2$ to the power $n$ and determine the size, chromatic number, clique number, independence number, and matching through associate classes of divisors of $2^n$ in $\mathbb{Z}_{2^n}[i]$. In addition, a few topological indices of the corresponding zero-divisor graph, are obtained.