# Two Short Proofs on Total Domination

Discussiones Mathematicae Graph Theory (2013)

- Volume: 33, Issue: 2, page 457-459
- ISSN: 2083-5892

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topAllan Bickle. "Two Short Proofs on Total Domination." Discussiones Mathematicae Graph Theory 33.2 (2013): 457-459. <http://eudml.org/doc/268215>.

@article{AllanBickle2013,

abstract = {A set of vertices of a graph G is a total dominating set if each vertex of G is adjacent to a vertex in the set. The total domination number of a graph Υt (G) is the minimum size of a total dominating set. We provide a short proof of the result that Υt (G) ≤ 2/3n for connected graphs with n ≥ 3 and a short characterization of the extremal graphs.},

author = {Allan Bickle},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {total domination},

language = {eng},

number = {2},

pages = {457-459},

title = {Two Short Proofs on Total Domination},

url = {http://eudml.org/doc/268215},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Allan Bickle

TI - Two Short Proofs on Total Domination

JO - Discussiones Mathematicae Graph Theory

PY - 2013

VL - 33

IS - 2

SP - 457

EP - 459

AB - A set of vertices of a graph G is a total dominating set if each vertex of G is adjacent to a vertex in the set. The total domination number of a graph Υt (G) is the minimum size of a total dominating set. We provide a short proof of the result that Υt (G) ≤ 2/3n for connected graphs with n ≥ 3 and a short characterization of the extremal graphs.

LA - eng

KW - total domination

UR - http://eudml.org/doc/268215

ER -

## References

top- [1] R.C. Brigham, J.R. Carrington and R.P. Vitray, Connected graphs with maximum total domination number , J. Combin. Comput. Combin. Math. 34 (2000) 81-96. Zbl0958.05100
- [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 Zbl0447.05039
- [3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, Inc, 1998). Zbl0890.05002

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