ArticleOriginal scientific text

Title

A note on domination parameters in random graphs

Authors 1, 2

Affiliations

  1. Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada, N2L 3C5
  2. Department of Mathematics, Ryerson University, Toronto, ON, Canada, M5B 2K3

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).

Keywords

domination, random graphs, independent domination, total domination

Bibliography

  1. N. Alon and J. Spencer, The Probabilistic Method (Wiley, New York, 2000).
  2. P.A. Dreyer, Applications and variations of domination in graphs, Ph.D. Dissertation, Department of Mathematics (Rutgers University, 2000).
  3. T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).
  4. T.W. Haynes, S.T. Hedetniemi and P.J. Slater (eds.), Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998).
  5. S. Janson, T. Łuczak and A. Ruciński, Random Graphs (John Wiley and Sons, New York, 2000), doi: 10.1002/9781118032718.
  6. C. Kaiser and K. Weber, Degrees and domination number of random graphs in the n-cube, Rostock. Math. Kolloq. 28 (1985) 18-32.
  7. K. Weber, Domination number for almost every graph, Rostock. Math. Kolloq. 16 (1981) 31-43.
  8. B. Wieland and A.P. Godbole, On the domination number of a random graph, The Electronic Journal of Combinatorics 8 (2001) #R37.
  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.
Pages:
335-343
Main language of publication
English
Received
2008-01-11
Accepted
2008-03-03
Published
2008
Exact and natural sciences