Home > Journals > TAG > Vol. 9 > Iss. 1 (2022)
Publication Date
February 2022
Abstract
Let $A$ be a nontrivial abelian group and $A^* = A \setminus \{0\}$. 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. 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 $\mathbb{Z}_p$-magic labelings (prime $p \geq 3$ ) for various graphs, without having to construct the $\mathbb{Z}_p$-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 $\mathbb{Z}_3$-magic labelings and give some results for various classes of graphs.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Low, Richard M. and Roberts, Dan
(2022)
"Application of the Combinatorial Nullstellensatz to Integer-magic Graph Labelings,"
Theory and Applications of Graphs: Vol. 9:
Iss.
1, Article 3.
DOI: 10.20429/tag.2022.090103
Available at:
https://digitalcommons.georgiasouthern.edu/tag/vol9/iss1/3