Two Short Proofs on Total Domination

Allan Bickle

Discussiones Mathematicae Graph Theory (2013)

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

Abstract

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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.

How to cite

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Allan 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

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  1. [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. [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. [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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