A note on domination parameters in random graphs

Anthony Bonato; Changping Wang

Discussiones Mathematicae Graph Theory (2008)

  • Volume: 28, Issue: 2, page 335-343
  • ISSN: 2083-5892

Abstract

top
Domination parameters in random graphs G(n,p), where p is a fixed real number in (0,1), are investigated. We show that with probability tending to 1 as n → ∞, the total and independent domination numbers concentrate on the domination number of G(n,p).

How to cite

top

Anthony Bonato, and Changping Wang. "A note on domination parameters in random graphs." Discussiones Mathematicae Graph Theory 28.2 (2008): 335-343. <http://eudml.org/doc/270563>.

@article{AnthonyBonato2008,
abstract = {Domination parameters in random graphs G(n,p), where p is a fixed real number in (0,1), are investigated. We show that with probability tending to 1 as n → ∞, the total and independent domination numbers concentrate on the domination number of G(n,p).},
author = {Anthony Bonato, Changping Wang},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {domination; random graphs; independent domination; total domination},
language = {eng},
number = {2},
pages = {335-343},
title = {A note on domination parameters in random graphs},
url = {http://eudml.org/doc/270563},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Anthony Bonato
AU - Changping Wang
TI - A note on domination parameters in random graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2008
VL - 28
IS - 2
SP - 335
EP - 343
AB - Domination parameters in random graphs G(n,p), where p is a fixed real number in (0,1), are investigated. We show that with probability tending to 1 as n → ∞, the total and independent domination numbers concentrate on the domination number of G(n,p).
LA - eng
KW - domination; random graphs; independent domination; total domination
UR - http://eudml.org/doc/270563
ER -

References

top
  1. [1] N. Alon and J. Spencer, The Probabilistic Method (Wiley, New York, 2000). Zbl0996.05001
  2. [2] P.A. Dreyer, Applications and variations of domination in graphs, Ph.D. Dissertation, Department of Mathematics (Rutgers University, 2000). 
  3. [3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). Zbl0890.05002
  4. [4] T.W. Haynes, S.T. Hedetniemi and P.J. Slater (eds.), Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998). Zbl0883.00011
  5. [5] S. Janson, T. Łuczak and A. Ruciński, Random Graphs (John Wiley and Sons, New York, 2000), doi: 10.1002/9781118032718. 
  6. [6] C. Kaiser and K. Weber, Degrees and domination number of random graphs in the n-cube, Rostock. Math. Kolloq. 28 (1985) 18-32. Zbl0605.05036
  7. [7] K. Weber, Domination number for almost every graph, Rostock. Math. Kolloq. 16 (1981) 31-43. Zbl0476.05067
  8. [8] B. Wieland and A.P. Godbole, On the domination number of a random graph, The Electronic Journal of Combinatorics 8 (2001) #R37. Zbl0989.05108
  9. [9] I.E. Zverovich and V.E. Zverovich, The domination parameters of cubic graphs, Graphs and Combinatorics 21 (2005) 277-288, doi: 10.1007/s00373-005-0608-1. Zbl1067.05053

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.