Vertices contained in all minimum paired-dominating sets of a tree

Xue-Gang Chen

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 1, page 407-417
  • ISSN: 0011-4642

Abstract

top
A set S of vertices in a graph G is called a paired-dominating set if it dominates V and S contains at least one perfect matching. We characterize the set of vertices of a tree that are contained in all minimum paired-dominating sets of the tree.

How to cite

top

Chen, Xue-Gang. "Vertices contained in all minimum paired-dominating sets of a tree." Czechoslovak Mathematical Journal 57.1 (2007): 407-417. <http://eudml.org/doc/31138>.

@article{Chen2007,
abstract = {A set $S$ of vertices in a graph $G$ is called a paired-dominating set if it dominates $V$ and $\langle S\rangle $ contains at least one perfect matching. We characterize the set of vertices of a tree that are contained in all minimum paired-dominating sets of the tree.},
author = {Chen, Xue-Gang},
journal = {Czechoslovak Mathematical Journal},
keywords = {domination number; paired-domination number; tree; domination number; paired-domination number; paired-dominating set; tree},
language = {eng},
number = {1},
pages = {407-417},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Vertices contained in all minimum paired-dominating sets of a tree},
url = {http://eudml.org/doc/31138},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Chen, Xue-Gang
TI - Vertices contained in all minimum paired-dominating sets of a tree
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 407
EP - 417
AB - A set $S$ of vertices in a graph $G$ is called a paired-dominating set if it dominates $V$ and $\langle S\rangle $ contains at least one perfect matching. We characterize the set of vertices of a tree that are contained in all minimum paired-dominating sets of the tree.
LA - eng
KW - domination number; paired-domination number; tree; domination number; paired-domination number; paired-dominating set; tree
UR - http://eudml.org/doc/31138
ER -

References

top
  1. 10.1137/0603052, SIAM J. Algebraic Discrete Math. 3 (1982), 511–522. (1982) MR0679645DOI10.1137/0603052
  2. 10.1002/(SICI)1097-0118(199907)31:3<163::AID-JGT2>3.0.CO;2-T, J. Graph Theory 31 (1999), 163–177. (1999) Zbl0931.05063MR1688945DOI10.1002/(SICI)1097-0118(199907)31:3<163::AID-JGT2>3.0.CO;2-T
  3. 10.1016/S0012-365X(02)00447-8, Discrete Math. 260 (2003), 37–44. (2003) MR1948372DOI10.1016/S0012-365X(02)00447-8
  4. Paired-domination in graphs, 32 (1998), Networks, 199–206. (1998) MR1645415
  5. 10.1016/S0012-365X(02)00451-X, Discrete Math. 260 (2003), 77–87. (2003) MR1948376DOI10.1016/S0012-365X(02)00451-X
  6. Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998. (1998) MR1605684
  7. Domination in Graphs: Advanced Topics, T. W. Haynes, S. T. Hedetniemi and P. J. Slater (eds.), Marcel Dekker, New York, 1998. (1998) Zbl0883.00011MR1605685

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.