Electronic Theses and Dissertations
Date
2024
Document Type
Thesis
Degree Name
Master of Science
Department
Mathematical Sciences
Committee Chair
Maarten De Boeck
Committee Member
David Grynkiewicz
Committee Member
Dheer Desai
Committee Member
Thomas Hagen
Abstract
The class of Group Divisible Generalized Petersen Graphs, GDGPs, comes from a line of generalizations of the Petersen Graph, which originated with the Generalized Petersen Graphs. We begin the thesis with a survey of some of these older generalizations in the first two chapters. Chapters three and four contain a summary of the results from [7], where GDGPs are introduced, including a proof of their regularity and an examination of vertex transitivity via several types of automorphisms. The final chapter contains original results: two Lemmas that make progress on a conjecture regarding vertex transitivity of GDGPs with a single inner cycle, and establishing necessary conditions for vertex transitivity among some other families based on inner cycle length.
Library Comment
Dissertation or thesis originally submitted to ProQuest.
Notes
Open access.
Recommended Citation
Molder, Noah, "Vertex Transitivity of Group Divisible Generalized Petersen Graphs" (2024). Electronic Theses and Dissertations. 3645.
https://digitalcommons.memphis.edu/etd/3645
Comments
Data is provided by the student.