Show simple item record  

dc.contributor.advisorDelbourgo, Daniel
dc.contributor.authorGilmore, Hamish Julian
dc.date.accessioned2015-06-09T02:14:12Z
dc.date.available2015-06-09T02:14:12Z
dc.date.issued2015
dc.identifier.citationGilmore, H. J. (2015). Algebraic Properties of Chromatic Polynomials and Their Roots (Thesis, Master of Science (MSc)). University of Waikato, Hamilton, New Zealand. Retrieved from https://hdl.handle.net/10289/9367en
dc.identifier.urihttps://hdl.handle.net/10289/9367
dc.description.abstractIn this thesis we examine chromatic polynomials from the viewpoint of algebraic number theory. We relate algebraic properties of chromatic polynomials of graphs to structural properties of those graphs for some simple families of graphs. We then compute the Galois groups of chromatic polynomials of some sub-families of an infinite family of graphs (denoted {Gp,q }) and prove a conjecture posed in [15] concerning the Galois groups of one specific sub-family. Finally we investigate a conjecture due to Peter Cameron [8] that says that for any algebraic integer α there is some n ∈ ℕ such that α + n is the root of some chromatic polynomial. We prove the conjecture for quadratic and cubic integers and provide strong computational evidence that it is true for quartic and quintic integers.
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/zip
dc.language.isoen
dc.publisherUniversity of Waikato
dc.rightsAll items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated.
dc.subjectchromatic
dc.subjectpolynomial
dc.subjectalgebraic
dc.subjectnumber
dc.subjecttheory
dc.titleAlgebraic Properties of Chromatic Polynomials and Their Roots
dc.typeThesis
thesis.degree.grantorUniversity of Waikato
thesis.degree.levelMasters
thesis.degree.nameMaster of Science (MSc)
dc.date.updated2015-02-12T21:12:01Z
pubs.place-of-publicationHamilton, New Zealanden_NZ


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record