For a subset of vertices S in a graph G, if v ∈ S and w ∈ V - S, then the vertex w is an external private neighbor of v (with respect to S) if the only neighbor of w in S is v. A dominating set S is a private dominating set if each v ∈ S has an external private neighbor. Bollóbas and Cockayne (Graph theoretic parameters concerning domination, independence and irredundance. J. Graph Theory 3 (1979) 241-250) showed that every graph without isolated vertices has a minimum dominating set which is also a private dominating set. We define a graph G to be a private domination graph if every minimum dominating set of G is a private dominating set. We give a constructive characterization of private domination trees.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-19455 |
| Date | 01 July 2006 |
| Creators | Haynes, Teresa, Henning, Michael A. |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
Page generated in 0.0026 seconds