An odd open dominating set of a graph is a subset of the graph’s vertices with the property that the open neighborhood of each vertex in the graph contains an odd number of vertices in the subset. An odd closed r-dominating set is a subset of the graph’s vertices with the property that the closed r-ball centered at each vertex in the graph contains an odd number of vertices in the subset. We first prove that the n-fold direct product of simple graphs has an odd open dominating set if and only if each factor has an odd open dominating set. Secondly, we prove that the n-fold strong product of simple graphs has an odd closed r-dominating set if and only if each factor has an odd closed r-dominating set.
Identifer | oai:union.ndltd.org:vcu.edu/oai:scholarscompass.vcu.edu:etd-3521 |
Date | 16 June 2011 |
Creators | Whisenant, Christopher |
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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