Now showing items 1-8 of 8

    • Algebraic Analysis of Vertex-Distinguishing Edge-Colorings 

      Clark, David (University of Waterloo, 2006)
      Vertex-distinguishing edge-colorings (vdec colorings) are a restriction of proper edge-colorings. These special colorings require that the sets of edge colors incident to every vertex be distinct. This is a relatively ...
    • Algebraic and combinatorial aspects of incidence groups and linear system non-local games arising from graphs 

      Paddock, Connor (University of Waterloo, 2019-06-06)
      To every linear binary-constraint system (LinBCS) non-local game, there is an associated algebraic object called the solution group. Cleve, Liu, and Slofstra showed that a LinBCS game has a perfect quantum strategy if and ...
    • Bipartite Quantum Walks and the Hamiltonian 

      Chen, Qiuting (University of Waterloo, 2023-09-26)
      We study a discrete quantum walk model called bipartite walks via a spectral approach. A bipartite walk is determined by a unitary matrix U, i.e., the transition matrix of the walk. For every transition matrix U, there is ...
    • Constructing Cospectral and Comatching Graphs 

      Wang, Xiaojing (University of Waterloo, 2019-07-18)
      The matching polynomial is a graph polynomial that does not only have interesting mathematical properties, but also possesses meaningful applications in physics and chemistry. For a simple graph, the matching polynomial ...
    • Discrete Quantum Walks on Graphs and Digraphs 

      Zhan, Hanmeng (University of Waterloo, 2018-09-26)
      This thesis studies various models of discrete quantum walks on graphs and digraphs via a spectral approach. A discrete quantum walk on a digraph $X$ is determined by a unitary matrix $U$, which acts on complex functions ...
    • Graph Coverings with Few Eigenvalues or No Short Cycles 

      Levit, Maxwell (University of Waterloo, 2023-05-18)
      This thesis addresses the extent of the covering graph construction. How much must a cover X resemble the graph Y that it covers? How much can X deviate from Y? The main statistics of X and Y which we will measure are their ...
    • The Graphs of HU+00E4ggkvist & Hell 

      Roberson, David E. (University of Waterloo, 2009-01-19)
      This thesis investigates HU+00E4ggkvist & Hell graphs. These graphs are an extension of the idea of Kneser graphs, and as such share many attributes with them. A variety of original results on many different properties of ...
    • Self-Complementary Arc-Transitive Graphs and Their Imposters 

      Mullin, Natalie Ellen (University of Waterloo, 2009-01-28)
      This thesis explores two infinite families of self-complementary arc-transitive graphs: the familiar Paley graphs and the newly discovered Peisert graphs. After studying both families, we examine a result of Peisert which ...

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