Application of the Combinatorial Nullstellensatz to Integer-magic Graph Labelings

Authors

Richard M. Low, San Jose State UniversityFollow
Dan Roberts, Illinois Wesleyan UniversityFollow

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 Ζ_p-magic labelings (prime p ≥ 3 ) for various graphs, without having to construct the Ζ_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 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