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      Algebraic Properties of Chromatic Polynomials and Their Roots

      Gilmore, Hamish Julian
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      Gilmore, 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/10289/9367
      Permanent Research Commons link: https://hdl.handle.net/10289/9367
      Abstract
      In 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.
      Date
      2015
      Type
      Thesis
      Degree Name
      Master of Science (MSc)
      Supervisors
      Delbourgo, Daniel
      Publisher
      University of Waikato
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      All items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated.
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      • Masters Degree Theses [2409]
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