Group vertex magicness of product graphs and trees

TL;DR

This paper investigates the conditions under which certain graphs, including trees and product graphs, exhibit group vertex magicness, providing characterizations and necessary conditions for these properties.

Contribution

It offers new necessary conditions for group vertex magicness in graphs with pendant vertices and characterizes this property in trees of small diameter and for specific infinite Abelian groups.

Findings

Necessary conditions for group vertex magicness in graphs with pendant vertices.

Characterization of group vertex magic trees of diameter up to 5.

Results for infinite Abelian groups with finitely many torsion elements.

Abstract

In this article, some necessary conditions of group vertex magicness of graphs with at least one pendant, group vertex magicness of product graphs, are proved. A characterization of group vertex magicness of trees of diameter up to 5. for all infinite Abelian groups with finitely many torsion elements, is also obtained.