Browsing Combinatorics and Optimization by Supervisor "Godsil, Chris"
Now showing items 112 of 12

Bipartite Quantum Walks and the Hamiltonian
(University of Waterloo, 20230926)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, 20190718)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 ... 
Covering Graphs and Equiangular Tight Frames
(University of Waterloo, 20160902)Recently, there has been huge attention paid to equiangular tight frames and their constructions, due to the fact that the relationship between these frames and quantum information theory was established. One of the problems ... 
Discrete Quantum Walks on Graphs and Digraphs
(University of Waterloo, 20180926)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 ... 
DistanceBiregular Graphs and Orthogonal Polynomials
(University of Waterloo, 20230915)This thesis is about distancebiregular graphs– when they exist, what algebraic and structural properties they have, and how they arise in extremal problems. We develop a set of necessary conditions for a distancebiregular ... 
Edge State Transfer
(University of Waterloo, 20190111)Let G be a graph and let t be a positive real number. Then the evolution of the continuous quantum walk defined on G is described by the transition matrix U(t)=exp(itH).The matrix H is called Hamiltonian. So far the most ... 
Hurwitz Trees and Tropical Geometry
(University of Waterloo, 20160121)The lifting problem in algebraic geometry asks when a finite group G acting on a curve defined over characteristic p > 0 lifts to characteristic 0. One object used in the study of this problem is the Hurwitz tree, which ... 
Matchings and Representation Theory
(University of Waterloo, 20181220)In this thesis we investigate the algebraic properties of matchings via representation theory. We identify three scenarios in different areas of combinatorial mathematics where the algebraic structure of matchings gives ... 
Quantum independence and chromatic numbers
(University of Waterloo, 20190828)In this thesis we are studying the cases when quantum independence and quantum chromatic numbers coincide with or differ from their classical counterparts. Knowing about the relation of chromatic numbers separation to the ... 
Quantum Walks and Pretty Good State transfer on Paths
(University of Waterloo, 20190823)Quantum computing is believed to provide many advantages over traditional computing, particularly considering the speed at which computations can be performed. One of the challenges that needs to be resolved in order to ... 
Quantum Walks on Oriented Graphs
(University of Waterloo, 20190111)This thesis extends results about periodicity and perfect state transfer to oriented graphs. We prove that if a vertex a is periodic, then elements of the eigenvalue support lie in Z √∆ for some squarefree negative ... 
State Transfer & Strong Cospectrality in Cayley Graphs
(University of Waterloo, 20220809)This thesis is a study of two graph properties that arise from quantum walks: strong cospectrality of vertices and perfect state transfer. We prove various results about these properties in Cayley graphs. We consider ...