Distance Antimagic Labeling of Zero-Divisor Graphs

Abstract

In this paper, we prove that for all $m\geq 1$ and $n=1$, the graph $ mΓ(\mathbb{Z}_9)+nΓ(\mathbb{Z}_4)$, for all $n\geq 1$, and $m=1$, the graph $m\overline{Γ(\mathbb{Z}_6)}+nΓ(\mathbb{Z}_9)$, for all $m\geq1$, $[mΓ(\mathbb{Z}_9)+Γ(\mathbb{Z}_4)]\times Γ(\mathbb{Z}_9)$, for all prime $m\geq3$, $Γ(\mathbb{Z}_6)\timesΓ(\mathbb{Z}_{2m})$ and $Γ(\mathbb{Z}_6)\timesΓ(\mathbb{Z}_{m^2})$ are all admit distance antimagic labeling.