In a graph G=(V,E), a subset S â V is a double dominating set if every vertex in V is dominated at least twice. The minimum cardinality of a double dominating set of G is the double domination number. A graph G is double domination edge critical if for any edge uv â E(GĖ ), the double domination number of G+uv is less than the double domination number of G. We investigate properties of double domination edge critical graphs. In particular, we characterize the double domination edge critical trees and cycles, graphs with double domination numbers of 3, and graphs with double domination numbers of 4 with maximum diameter.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etd-3541 |
| Date | 06 May 2006 |
| Creators | Thacker, Derrick Wayne |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Electronic Theses and Dissertations |
| Rights | Copyright by the authors. |
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