Trees with unique minimum total dominating sets
Teresa W. Haynes ; Michael A. Henning
Discussiones Mathematicae Graph Theory, Tome 22 (2002), p. 233-246 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

A set S of vertices of a graph G is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. We provide three equivalent conditions for a tree to have a unique minimum total dominating set and give a constructive characterization of such trees.

Publié le : 2002-01-01
EUDML-ID : urn:eudml:doc:270568 
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1172,
     author = {Teresa W. Haynes and Michael A. Henning},
     title = {Trees with unique minimum total dominating sets},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {22},
     year = {2002},
     pages = {233-246},
     zbl = {1031.05095},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1172}
}

Teresa W. Haynes; Michael A. Henning. Trees with unique minimum total dominating sets. Discussiones Mathematicae Graph Theory, Tome 22 (2002) pp. 233-246. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1172/

[000] [1] G. Chartrand and L. Lesniak, Graphs & Digraphs, third edition (Chapman & Hall, London, 1996).

[001] [2] E.J. Cockayne, R.M. Dawes and S.T. Hedetniemi, Total domination in graphs, Networks 10 (1980) 211-219, doi: 10.1002/net.3230100304. | Zbl 0447.05039

[002] [3] E. Cockayne, M.A. Henning and C.M. Mynhardt, Vertices contained in every minimum total dominating set of a tree, to appear in Discrete Math. | Zbl 1013.05054

[003] [4] O. Favaron, M.A. Henning, C.M. Mynhardt and J. Puech, Total domination in graphs with minimum degree three, J. Graph Theory 34 (2000) 9-19, doi: 10.1002/(SICI)1097-0118(200005)34:1<9::AID-JGT2>3.0.CO;2-O

[004] [5] G. Gunther, B. Hartnell, L.R. Markus and D. Rall, Graphs with unique minimum dominating sets, Congr. Numer. 101 (1994) 55-63. | Zbl 0836.05045

[005] [6] G. Gunther, B. Hartnell and D. Rall, Graphs whose vertex independence number is unaffected by single edge addition or deletion, Discrete Appl. Math. 46 (1993) 167-172, doi: 10.1016/0166-218X(93)90026-K. | Zbl 0792.05116

[006] [7] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). | Zbl 0890.05002

[007] [8] T.W. Haynes, S.T. Hedetniemi and P.J. Slater (eds), Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998). | Zbl 0883.00011

[008] [9] M.A. Henning, Graphs with large total domination number, J. Graph Theory 35 (2000) 21-45, doi: 10.1002/1097-0118(200009)35:1<21::AID-JGT3>3.0.CO;2-F | Zbl 0959.05089

[009] [10] G. Hopkins and W. Staton, Graphs with unique maximum independent sets, Discrete Math. 57 (1985) 245-251, doi: 10.1016/0012-365X(85)90177-3. | Zbl 0583.05034