#### Sponsor

Mihai Caragiu, PhD

Ohio Northern University

Mathematics, Science, Technology, and Mathematics

m-caragiu@onu.edu

#### Advisor(s)

Mihai Caragiu, PhD

Ohio Northern University

Mathematics, Science, Technology, and Mathematics

m-caragiu@onu.edu

#### Document Type

Video

#### Start Date

23-4-2021 9:00 AM

#### Abstract

The characteristic polynomial is one of the most important invariants of a graph, with applications in everything from molecular chemistry to electrical engineering. However, despite its simple geometric structure, nobody has ever found a formula for the characteristic polynomial of the square grid graph. This presentation seeks to take a closer look into the matter to see if there are any patterns in the functions and if, in fact, a general formula can even be defined.

#### Award

First place recipient for the School of Science, Technology and Mathematics Choice Award

#### Recommended Citation

Kemats, Aaron X., "On the Characteristic Polynomial of the Square Grid Graph" (2021). *ONU Student Research Colloquium*. 16.

https://digitalcommons.onu.edu/student_research_colloquium/2021/papers/16

#### Open Access

Available to all.

On the Characteristic Polynomial of the Square Grid Graph

The characteristic polynomial is one of the most important invariants of a graph, with applications in everything from molecular chemistry to electrical engineering. However, despite its simple geometric structure, nobody has ever found a formula for the characteristic polynomial of the square grid graph. This presentation seeks to take a closer look into the matter to see if there are any patterns in the functions and if, in fact, a general formula can even be defined.

## Notes

This presentation is part of the Honors Capstone Enhancement Presentation series.