Applying the Combinatorial Nullstellensatz To Integer-Magic Labelings; Hartke Magic-ness
Major
Physics
Second Major
Mathematics
Submission Type
Poster
Area of Study or Work
Mathematics
Faculty Advisor
Dan Roberts
Location
CNS Atrium
Start Date
4-11-2026 8:30 AM
End Date
4-11-2026 9:45 AM
Abstract
In this project we are using Computational Experimentation methods to identify whether or not graphs contain a magic labeling. This method is computing the Hartke polynomial of a graph, and then using the Combinatorial Nullstellensatz to detect if that graph has an integer-magic labeling. Our goal is to prove that for any graph of order 6 and beyond, there is a graph of that order which has a magic labeling that is detectable via its Hartke polynomial. As the order of the graph grows, the required computation grows, therefore we perform a qualitative analysis on smaller order graphs by examining the substructures and how they interact with each other. The goal is to gain insight into the Hartke polynomial of larger order graphs built with these same substructures.
Applying the Combinatorial Nullstellensatz To Integer-Magic Labelings; Hartke Magic-ness
CNS Atrium
In this project we are using Computational Experimentation methods to identify whether or not graphs contain a magic labeling. This method is computing the Hartke polynomial of a graph, and then using the Combinatorial Nullstellensatz to detect if that graph has an integer-magic labeling. Our goal is to prove that for any graph of order 6 and beyond, there is a graph of that order which has a magic labeling that is detectable via its Hartke polynomial. As the order of the graph grows, the required computation grows, therefore we perform a qualitative analysis on smaller order graphs by examining the substructures and how they interact with each other. The goal is to gain insight into the Hartke polynomial of larger order graphs built with these same substructures.