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Washington State
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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.