Browsing Combinatorics and Optimization by Subject "algebraic graph theory"
Now showing items 1-8 of 8
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Algebraic Analysis of Vertex-Distinguishing Edge-Colorings
(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
(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
(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
(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
(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
(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
(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
(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 ...