The Domination Number of K 3 n
John Georges; Jianwei Lin; David Mauro
Discussiones Mathematicae Graph Theory (2014)
- Volume: 34, Issue: 3, page 629-632
- ISSN: 2083-5892
Access Full Article
topAbstract
topHow to cite
topJohn Georges, Jianwei Lin, and David Mauro. " The Domination Number of K 3 n ." Discussiones Mathematicae Graph Theory 34.3 (2014): 629-632. <http://eudml.org/doc/267624>.
@article{JohnGeorges2014,
abstract = {Let K3n denote the Cartesian product Kn□Kn□Kn, where Kn is the complete graph on n vertices. We show that the domination number of K3n is [...]},
author = {John Georges, Jianwei Lin, David Mauro},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {Cartesian product; dominating set; domination number},
language = {eng},
number = {3},
pages = {629-632},
title = { The Domination Number of K 3 n },
url = {http://eudml.org/doc/267624},
volume = {34},
year = {2014},
}
TY - JOUR
AU - John Georges
AU - Jianwei Lin
AU - David Mauro
TI - The Domination Number of K 3 n
JO - Discussiones Mathematicae Graph Theory
PY - 2014
VL - 34
IS - 3
SP - 629
EP - 632
AB - Let K3n denote the Cartesian product Kn□Kn□Kn, where Kn is the complete graph on n vertices. We show that the domination number of K3n is [...]
LA - eng
KW - Cartesian product; dominating set; domination number
UR - http://eudml.org/doc/267624
ER -
References
top- [1] T.Y. Chang, Domination number of grid graphs, Ph.D. Thesis, (Department of Mathematics, University of South Florida, 1992).
- [2] T.Y. Chang and W.E. Clark, The domination numbers of the 5 × n and 6 × n grid graphs, J. Graph Theory 17 (1993) 81-108. doi:10.1002/jgt.3190170110[Crossref] Zbl0780.05030
- [3] M.H. El-Zahar and R.S. Shaheen, On the domination number of the product of two cycles, Ars Combin. 84 (2007) 51-64. Zbl1212.05192
- [4] M.H. El-Zahar and R.S. Shaheen, The domination number of C8 □Cn and C9 □Cn, J. Egyptian Math. Soc. 7 (1999) 151-166. Zbl0935.05070
- [5] D. Gon¸calves, A. Pinlou, M. Rao and S. Thomass´e, The domination number of grids, SIAM J. Discrete Math. 25 (2011) 1443-1453. doi:10.1137/11082574[Crossref][WoS]
- [6] F. Harary and M. Livingston, Independent domination in hypercubes, Appl. Math. Lett. 6 (1993) 27-28. doi:10.1016/0893-9659(93)90027-K[Crossref] Zbl0780.05031
- [7] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, 1998). Zbl0890.05002
- [8] M.S. Jacobson and L.F. Kinch, On the domination number of the products of graphs I, Ars Combin. 18 (1983) 33-44. Zbl0566.05050
- [9] S. Klavˇzar and N. Seifter, Dominating Cartesian products of cycles, Discrete Appl. Math. 59 (1995) 129-136. doi:10.1016/0166-218X(93)E0167-W[Crossref] Zbl0824.05037
- [10] K.-J. Pai and W.-J. Chiu, A note on ”On the power dominating set of hypercubes”, in: Proceedings of the 29th Workshop on Combinatorial Mathematics and Comput- ing Theory, National Taipei College of Business, Taipei, Taiwan April 27-28, (2012) 65-68.
- [11] R.S. Shaheen, On the domination number of m × n toroidal grid graphs, Congr. Numer. 146 (2000) 187-200. Zbl0976.05045
- [12] V.G Vizing, Some unsolved problems in graph theory, Uspekhi Mat. Nauk, 23 (6 (144)) (1968) 117-134. Zbl0177.52301
- [13] V.G Vizing, The Cartesian product of graphs, Vy˘cisl. Sistemy 9 (1963) 30-43.
- [14] D.B. West, Introduction to Graph Theory (Prentice Hall, 2001)
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.