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.
| Identifer | oai:union.ndltd.org:vcu.edu/oai:scholarscompass.vcu.edu:etd-5937 |
| Date | 01 January 2017 |
| Creators | Crenshaw, Cameron M |
| Publisher | VCU Scholars Compass |
| Source Sets | Virginia Commonwealth University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Theses and Dissertations |
| Rights | © The Author |
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