Remarks on restrained domination and total restrained domination in graphs

Bohdan Zelinka

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 2, page 393-396
  • ISSN: 0011-4642

Abstract

top
The restrained domination number γ r ( G ) and the total restrained domination number γ t r ( G ) of a graph G were introduced recently by various authors as certain variants of the domination number γ ( G ) of ( G ) . A well-known numerical invariant of a graph is the domatic number d ( G ) which is in a certain way related (and may be called dual) to γ ( G ) . The paper tries to define analogous concepts also for the restrained domination and the total restrained domination and discusses the sense of such new definitions.

How to cite

top

Zelinka, Bohdan. "Remarks on restrained domination and total restrained domination in graphs." Czechoslovak Mathematical Journal 55.2 (2005): 393-396. <http://eudml.org/doc/30952>.

@article{Zelinka2005,
abstract = {The restrained domination number $\gamma ^r (G)$ and the total restrained domination number $\gamma ^r_t (G)$ of a graph $G$ were introduced recently by various authors as certain variants of the domination number $\gamma (G)$ of $(G)$. A well-known numerical invariant of a graph is the domatic number $d (G)$ which is in a certain way related (and may be called dual) to $\gamma (G)$. The paper tries to define analogous concepts also for the restrained domination and the total restrained domination and discusses the sense of such new definitions.},
author = {Zelinka, Bohdan},
journal = {Czechoslovak Mathematical Journal},
keywords = {domination number; domatic number; total domination number; total domatic number; restrained domination number; restrained domatic number; total restrained domination number; total restrained domatic number; domination number; domatic number; total domination number; total domatic number; restrained domination number},
language = {eng},
number = {2},
pages = {393-396},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Remarks on restrained domination and total restrained domination in graphs},
url = {http://eudml.org/doc/30952},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Zelinka, Bohdan
TI - Remarks on restrained domination and total restrained domination in graphs
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 2
SP - 393
EP - 396
AB - The restrained domination number $\gamma ^r (G)$ and the total restrained domination number $\gamma ^r_t (G)$ of a graph $G$ were introduced recently by various authors as certain variants of the domination number $\gamma (G)$ of $(G)$. A well-known numerical invariant of a graph is the domatic number $d (G)$ which is in a certain way related (and may be called dual) to $\gamma (G)$. The paper tries to define analogous concepts also for the restrained domination and the total restrained domination and discusses the sense of such new definitions.
LA - eng
KW - domination number; domatic number; total domination number; total domatic number; restrained domination number; restrained domatic number; total restrained domination number; total restrained domatic number; domination number; domatic number; total domination number; total domatic number; restrained domination number
UR - http://eudml.org/doc/30952
ER -

References

top
  1. 10.1007/s10587-005-0012-2, Czechoslovak Math.  J. 55(130) (2005), 165–173. (2005) MR2121664DOI10.1007/s10587-005-0012-2
  2. 10.1002/net.3230070305, Networks 7 (1977), 247–261. (1977) MR0483788DOI10.1002/net.3230070305
  3. 10.1002/net.3230100304, Networks 10 (1980), 211–219. (1980) MR0584887DOI10.1002/net.3230100304
  4. 10.1016/S0012-365X(99)00016-3, Discrete Math. 203 (1999), 61–69. (1999) MR1696234DOI10.1016/S0012-365X(99)00016-3
  5. Fundamentals of Domination in Graphs, Marcel Dekker Inc., New York-Basel-Hong Kong, 1998. (1998) MR1605684
  6. Graphs with large restrained domination number, Discrete Math. 197/198 (1999), 415–429. (1999) Zbl0932.05070MR1674878

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.