Home > Journals > TAG > Vol. 9 > Iss. 1 (2022)
Publication Date
February 2022
Abstract
Let A be a nontrivial 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. 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 Ζp-magic labelings (prime p ≥ 3 ) for various graphs, without having to construct the Ζp-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 Ζ3-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
Supplemental DOIs