Date Thesis Awarded

12-2014

Document Type

Honors Thesis

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Charles Johnson

Committee Member

M. Sean Tarter

Committee Member

Anke van Zuylen

Abstract

Let A be a real symmetric matrix whose graph is a tree, T. If T is a linear tree (meaning all vertices with degree 3 or larger lie on the same induced path), then we can use a ”Linear Superposition Principle” to determine all possible multiplicities of eigenvalues of A. If T is a nonlinear tree, we must use other ad hoc methods. I utilize these methods to compute all possible multiplicity lists of trees on 12 vertices, and augment an existing multiplicities database. This database allows us to examine of the effects that the structure of tree can have on a multiplicity list. Then, I investigate the enumeration of linear and nonlinear trees, and examine the ratio of nonlinear trees to total trees.

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