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.

Notes

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

Award

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

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Open Access

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Apr 23rd, 9:00 AM

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.