# Trees with unique minimum total dominating sets

Teresa W. Haynes; Michael A. Henning

Discussiones Mathematicae Graph Theory (2002)

- Volume: 22, Issue: 2, page 233-246
- ISSN: 2083-5892

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topTeresa W. Haynes, and Michael A. Henning. "Trees with unique minimum total dominating sets." Discussiones Mathematicae Graph Theory 22.2 (2002): 233-246. <http://eudml.org/doc/270568>.

@article{TeresaW2002,

abstract = {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.},

author = {Teresa W. Haynes, Michael A. Henning},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {domination; total domination},

language = {eng},

number = {2},

pages = {233-246},

title = {Trees with unique minimum total dominating sets},

url = {http://eudml.org/doc/270568},

volume = {22},

year = {2002},

}

TY - JOUR

AU - Teresa W. Haynes

AU - Michael A. Henning

TI - Trees with unique minimum total dominating sets

JO - Discussiones Mathematicae Graph Theory

PY - 2002

VL - 22

IS - 2

SP - 233

EP - 246

AB - 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.

LA - eng

KW - domination; total domination

UR - http://eudml.org/doc/270568

ER -

## References

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- [7] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). Zbl0890.05002
- [8] T.W. Haynes, S.T. Hedetniemi and P.J. Slater (eds), Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998). Zbl0883.00011
- [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 Zbl0959.05089
- [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. Zbl0583.05034

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