A Conjecture on Zero-sum 3-magic Labeling of 5-regular Graphs

TL;DR

This paper proves that every 5-regular graph can be labeled with three numbers such that the sum at each vertex is zero, confirming a previously posed conjecture in graph theory.

Contribution

It establishes that all 5-regular graphs admit a zero-sum 3-magic labeling, resolving an open conjecture in the field.

Findings

All 5-regular graphs have zero-sum 3-magic labelings.

Confirmed the conjecture by Akbari, Rahmati, and Zare.

Provides a constructive proof for the labeling existence.

Abstract

In this paper, we obtained that every 5-regular graph admits a zero-sum 3-magic labeling, which give an affirmative answer to a conjecture proposed by Saieed Akbari, Farhad Rahmati and Sanaz Zare in $Electron.$ $J.$ $Combin.$.