Date of Award

5-2025

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

Mathematics

Thesis Sponsor/Dissertation Chair/Project Chair

Jonathan Cutler

Committee Member

Deepak Bal

Committee Member

Aihua Li

Abstract

This thesis investigates recent results and conjectures regarding inversion numbers of oriented graphs. We define the inversion number of an oriented graph G as the minimum size of a decycling family of subsets of vertices of G. We focus on three areas: the maximum inversion number of a graph on n vertices, the inversion numbers of dijoins of two oriented graphs, and computational algorithms for deciding the inversion number. The main contribution of this thesis is a proposed construction of a graph with higher inversion number than that of any other currently known construction. We also provide explicit, rather than asymptotic, bounds on the inversion numbers of graphs up to 11 vertices.

File Format

PDF

Download

Included in

Mathematics Commons

Share

COinS