DOI
https://doi.org/10.25772/K6SD-EF93
Defense Date
2017
Document Type
Thesis
Degree Name
Master of Science
Department
Mathematical Sciences
First Advisor
Richard Hammack
Abstract
In their recent paper ``Edge-transitive products," Hammack, Imrich, and Klavzar showed that the direct product of connected, non-bipartite graphs is edge-transitive if and only if both factors are edge-transitive, and at least one is arc-transitive. However, little is known when the product is bipartite. This thesis extends this result (in part) for the case of bipartite graphs using a new technique called "stacking." For R-thin, connected, bipartite graphs A and B, we show that A x B is arc-transitive if and only if A and B are both arc-transitive. Further, we show A x B is edge-transitive only if at least one of A, B is also edge-transitive, and give evidence that strongly suggests that in fact both factors must be edge-transitive.
Rights
© The Author
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
5-11-2017