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.
@article{bwmeta1.element.doi-10_7151_dmgt_1655,
author = {Allan Bickle},
title = {Two Short Proofs on Total Domination},
journal = {Discussiones Mathematicae Graph Theory},
volume = {33},
year = {2013},
pages = {457-459},
zbl = {1293.05255},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1655}
}
Allan Bickle. Two Short Proofs on Total Domination. Discussiones Mathematicae Graph Theory, Tome 33 (2013) pp. 457-459. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1655/
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