Distance Antimagic Labeling of Zero-Divisor Graphs

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