Distance Antimagic Labeling of Zero-Divisor Graphs

TL;DR

This paper proves that various complex zero-divisor graphs derived from modular rings admit distance antimagic labelings, expanding understanding of graph labelings in algebraic structures.

Contribution

It establishes that a wide class of zero-divisor graphs from modular rings have distance antimagic labelings, providing new results in algebraic graph theory.

Findings

Several classes of zero-divisor graphs admit distance antimagic labelings.

The results apply to graphs constructed from rings like inite rings and their products.

New theoretical proofs for the antimagic properties of these graphs.

Abstract

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