Abstract

This thesis is separated into two parts: threshold graphs and inertia sets. First we present an algorithmic approach to finding the minimum rank of threshold graphs and then progress to counting the number of threshold graphs with a specific minimum rank. Second, we find an algorithmic and more automated way of determining the inertia set of graphs with seven or fewer vertices using theorems and lemmata found in previous papers. Inertia sets are a relaxation of the inverse eigenvalue problem. Instead of determining all the possible eigenvalues that can be obtained by matrices with a specific zero/nonzero pattern we restrict to counting the number of positive and negative eigenvalues.

Degree

MS

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

http://lib.byu.edu/about/copyright/

Date Submitted

2013-12-17

Document Type

Thesis

Handle

http://hdl.lib.byu.edu/1877/etd6700

Keywords

threshold graphs, minimum rank, inertia sets

Included in

Mathematics Commons

Share

COinS