Washington State
University
Combinatorics, Linear Algebra and Number Theory Seminar
Department of Mathematics and Statistics
WEBS 11
October 3, Monday, 4:10 - 5:00 PM
Paula Kimmerling
Department of Mathematics and Statistics
Washington State University
Combinatorics, Linear Algebra and Number Theory Seminar
Department of Mathematics and Statistics
WEBS 11
October 3, Monday, 4:10 - 5:00 PM
Paula Kimmerling
Department of Mathematics and Statistics
Washington State University
Title: Continuous-Time Quantum Walks on Dutch
Windmill Graphs
Abstract: We will introduce the concept of a continuous-time quantum walk on a graph and describe what has been studied prior. For our work, we’ve focused on the rank of matrices associated with these graphs when the graphs have repeated eigenvalues. Dutch Windmill graphs provide one such family. We’ve combined several different proof methods to show that a particular matrix associated with a given Dutch Windmill graph is equal to a formula which is about half of its full rank. Detailing what we mean by “about”, we’ll also show how Dutch Windmill graphs are related to Path and Star graphs, as well as describe a recursion property that the eigenvectors possess.
Abstract: We will introduce the concept of a continuous-time quantum walk on a graph and describe what has been studied prior. For our work, we’ve focused on the rank of matrices associated with these graphs when the graphs have repeated eigenvalues. Dutch Windmill graphs provide one such family. We’ve combined several different proof methods to show that a particular matrix associated with a given Dutch Windmill graph is equal to a formula which is about half of its full rank. Detailing what we mean by “about”, we’ll also show how Dutch Windmill graphs are related to Path and Star graphs, as well as describe a recursion property that the eigenvectors possess.