Calculating and Preserving Star Sets and Star Complements of General Matrices

This thesis presents several results relating to star sets and star complements of graphs. While a method for calculating star sets and star complements involving pro- jection matrices has been known since their introduction, a second method involving determinants is demonstrated and shown to be equivalent to the rst method. Some of the theory for star sets and star complements is expanded to general diagonalizable matrices, regardless of symmetry. The concept of preserving star sets between two general matrices is introduced and shown to be an equivalence relation, and attempts are made to classify what types of matrices can preserve the star sets of a general matrix. Finally, we determine some results for general matrices that occur when star set preservation overlaps with other equivalence relations.

Name thesis:degree_name

Master of Science (MSc)

Level thesis:degree_level

Master's

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

Faculty of Graduate Studies and Research, University of Regina

Year dc:date.issued

2017

Author dc:creator

• Bergen, Ryan Paul

Advisor dc:contributor.advisor

• Fallat, Shaun

Committee member dc:contributor.committeemember

• Meagher, Karen

Language dc:language.iso

en

DOI

https://doi.org/10.82465/4060

OAI identifier oai:identifier

oai:uregina.scholaris.ca:10294/8447