#### Title

The Minimum Number of Multiplicity 1 Eigenvalues among Real Symmetric Matrices whose Graph is a Tree

#### Date Thesis Awarded

5-2021

#### Access Type

Honors Thesis -- Open Access

#### Degree Name

Bachelors of Science (BS)

#### Department

Mathematics

#### Advisor

Charles Johnson

#### Committee Members

Eric Swartz

Carl Moody

#### Abstract

For a tree T, U(T) denotes the minimum number of eigenvalues of multiplicity 1 among all real symmetric matrices whose graph is T. It is known that U(T) >= 2. A tree is linear if all its vertices of degree at least 3 lie on a single induced path, and k-linear if there are k of these high degree vertices. If T′ is a linear tree resulting from the addition of 1 vertex to T, we show that |U(T′)−U(T)|

#### Recommended Citation

Ding, Wenxuan, "The Minimum Number of Multiplicity 1 Eigenvalues among Real Symmetric Matrices whose Graph is a Tree" (2021). *Undergraduate Honors Theses.* Paper 1725.

https://scholarworks.wm.edu/honorstheses/1725