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

Abstract

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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.

How to cite

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Teresa 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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  1. [1] G. Chartrand and L. Lesniak, Graphs & Digraphs, third edition (Chapman & Hall, London, 1996). 
  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] 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. Zbl1013.05054
  4. [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 
  5. [5] G. Gunther, B. Hartnell, L.R. Markus and D. Rall, Graphs with unique minimum dominating sets, Congr. Numer. 101 (1994) 55-63. Zbl0836.05045
  6. [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. Zbl0792.05116
  7. [7] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). Zbl0890.05002
  8. [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. [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. [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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