Pancyclic zero divisor graph over the ring ${\mathbb{Z}}_n[i]$

Abstract

Let $\Gamma ({\mathbb{Z}}_n[i])$ be the zero divisor graph over the ring ${\mathbb{Z}}_n[i]$. In this article, we study pancyclic properties of $\Gamma ({\mathbb{Z}}_n[i])$ and $\overline{\Gamma ({\mathbb{Z}}_n[i])}$ for different $n$. Also, we prove some results in which $L(\Gamma ({\mathbb{Z}}_n[i]))$ and $\overline{L(\Gamma ({\mathbb{Z}}_n[i]))}$ to be pancyclic for different values of $n$.