Degree Type

Dissertation

Date of Award

2021

Degree Name

Doctor of Philosophy

Department

Mathematics

Major

Mathematics

First Advisor

Steve Butler

Abstract

A graph is a collection of objects (vertices) and connections between the objects (edges). Graphs can be associated with matrices by assigning matrix entries corresponding to the graph structure. As the graph grows large so does the matrix making it difficult to understand the graph's properties. The spectrum (multi-set of eigenvalues) of a matrix for a graph gives a snapshot of the graph structure independent of labeling. We know not all structural properties are captured by the spectrum by the existence of pairs of graphs that share a spectrum (cospectral graphs). In this dissertation, we investigate cospectrality for several graph matrices as well as discuss spectral properties of two recent matrix variants.

DOI

https://doi.org/10.31274/etd-20210609-106

Copyright Owner

Kate Lorenzen

Language

en

File Format

application/pdf

File Size

124 pages

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