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. William & Mary. Paper 1725.
https://scholarworks.wm.edu/honorstheses/1725
