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

TL;DR

This paper investigates the pancyclic properties of zero divisor graphs over the ring of Gaussian integers modulo n, including their complements and line graphs, for various values of n.

Contribution

It introduces new results on the pancyclicity of zero divisor graphs and their line graphs over z_n[i] for different n, expanding understanding in algebraic graph theory.

Findings

Zero divisor graphs over z_n[i] can be pancyclic for certain n.

The complements of these graphs also exhibit pancyclic properties.

Line graphs of these zero divisor graphs are pancyclic for specific n.

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 $n$.