Distance Antimagic Labeling of Zero-Divisor Graphs

Abstract

In this paper, we prove that for all $m\ge 1$ and $n=1$, the graph $m\Gamma ({\mathbb{Z}}_9)+n\Gamma ({\mathbb{Z}}_4)$, for all $n\ge 1$, and $m=1$, the graph $m\overline{\Gamma ({\mathbb{Z}}_6)}+n\Gamma ({\mathbb{Z}}_9)$, for all $m\ge 1$, $[m\Gamma ({\mathbb{Z}}_9)+\Gamma ({\mathbb{Z}}_4)]\times \Gamma ({\mathbb{Z}}_9)$, for all prime $m\ge 3$, $\Gamma ({\mathbb{Z}}_6)\times \Gamma ({\mathbb{Z}}_{2m})$ and $\Gamma ({\mathbb{Z}}_6)\times \Gamma ({\mathbb{Z}}_{m^2})$ are all admit distance antimagic labeling.