### On Group-Vertex-Magic Labeling of Simple Graphs

Muhammad Husnul Khuluq, Vira Hari Krisnawati, Noor Hidayat

#### Abstract

Let A be an Abelian group with identity 0. The A-vertex-magic labeling of a graph G is a mapping from the set of vertices in G to A-{0} such that the sum of the labels of every open neighborhood vertex of v is equal, for every vertex v in G. In this article, we discuss group-vertex-magic labeling of some simple graphs by using the Abelian group Zk, with natural numbers k>1. We investigated some classes of simple graphs are path graphs, complete graphs, cyclic graphs, and star graphs. The method we used in this article is literature study and then developing the properties of vertex-magic labeling of some simple graphs, that are path graphs, complete graphs, cyclic graphs, and star graphs. We obtain that complete graphs, cyclic graphs, and star graphs have Zk-vertex-magic labeling, while path graphs have vertex-magic labeling only for n=2,3.

#### Keywords

Abelian group; group-vertex-magic labeling; simple graphs

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DOI: https://doi.org/10.18860/ca.v8i2.23621