Enumeration, isomorphism and Hamiltonicity of Cayley graphs: 2-generated and cubic

Files

Effler_2002_thesis.pdf (2.91 MB)

Date

2008-11-25T17:46:42Z

Authors

Effler, Scott

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

This thesis explores 2-generated and cubic Cayley graphs. All 2-generated Cayley graphs with generators from Sn where n < 9, were generated. Further, 3-generated cubic Cayley graphs, where n < 7, were also generated. Among these, the cubic Cayley graphs with up to 40320 vertices were tested for various properties including Hamiltonicity and diameter. These results are available on the internet in easy to read tables. The motivation for the testing of Cayley graphs for Hamiltonicity was the conjecture that states that every connected Cayley graph is Hamiltonian. New enumeration results are presented for various classes of 2-generated Cayley graphs. Previously known enumeration results are presented for cubic Cayley graphs.Finally, isomorphism and color isomorphism of 2-generated and cubic Cay­ley graphs is explored. Numerous new results are presented. All algorithms used in this thesis are explained in full.

Description

Keywords

Hamiltonicity, Cayley graphs

Citation

URI

http://hdl.handle.net/1828/1265

Collections

ETD (Electronic Theses and Dissertations)
Theses (Computer Science)
 
University of Victoria Libraries

We acknowledge and respect the Lək̓ʷəŋən (Songhees and Esquimalt) Peoples on whose territory the university stands, and the Lək̓ʷəŋən and W̱SÁNEĆ Peoples whose historical relationships with the land continue to this day.