Publication Date

2-1-2022

Document Type

Article

Publication Title

Theory and Applications of Graphs

Volume

9

Issue

1

DOI

10.20429/tag.2022.090103

Abstract

Let A be a nontrivial additive abelian group and A* = A\{0}. A graph is A-magic if there exists an edge labeling f using elements of A* which induces a constant vertex labeling of the graph. Here, the induced label on a vertex is obtained by calculating the sum of the edge labels adjacent to that vertex. Such a labeling f is called an A-magic labeling and the constant value of the induced vertex labeling is called an A-magic value. In this paper, we use the Combinatorial Nullstellensatz to show the existence of Zp-magic labelings (prime p ≥ 3) for various graphs, without having to construct the Zp-magic labelings. Through many examples, we illustrate the usefulness and limitations in applying the Combinatorial Nullstellensatz to the integer-magic labeling problem. Finally, we focus on Z3-magic labelings and give some results for various classes of graphs.

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Department

Mathematics and Statistics

Download

Share

COinS