ArticleOriginal scientific text
Title
A note on domination parameters in random graphs
Authors 1, 2
Affiliations
- Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada, N2L 3C5
- 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
- N. Alon and J. Spencer, The Probabilistic Method (Wiley, New York, 2000).
- P.A. Dreyer, Applications and variations of domination in graphs, Ph.D. Dissertation, Department of Mathematics (Rutgers University, 2000).
- T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).
- T.W. Haynes, S.T. Hedetniemi and P.J. Slater (eds.), Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998).
- S. Janson, T. Łuczak and A. Ruciński, Random Graphs (John Wiley and Sons, New York, 2000), doi: 10.1002/9781118032718.
- C. Kaiser and K. Weber, Degrees and domination number of random graphs in the n-cube, Rostock. Math. Kolloq. 28 (1985) 18-32.
- K. Weber, Domination number for almost every graph, Rostock. Math. Kolloq. 16 (1981) 31-43.
- B. Wieland and A.P. Godbole, On the domination number of a random graph, The Electronic Journal of Combinatorics 8 (2001) #R37.
- 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.