Given a graph with domination number γ, we find bounds on the maximum number of minimum dominating sets. First, for γ≥3, we obtain lower bounds on the number of γ-sets that do not dominate a graph on n vertices. Then, we show that γ-fold lexicographic product of the complete graph on n1/γ vertices has domination number γ and γn-O(nγ-γ/1) dominating sets of size γ. Finally, we see that a certain random graph has, with high probability, (i) domination number γ; and (ii) all but o(nγ) of its γ-sets being dominating.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-16299 |
| Date | 06 May 2016 |
| Creators | Connolly, Samuel, Gabor, Zachary, Godbole, Anant, Kay, Bill, Kelly, Thomas |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
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