In this note the split domination number of the Cartesian product of two paths is considered. Our results are related to [2] where the domination number of Pₘ ☐ Pₙ was studied. The split domination number of P₂ ☐ Pₙ is calculated, and we give good estimates for the split domination number of Pₘ ☐ Pₙ expressed in terms of its domination number.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1262,
author = {Maciej Zwierzchowski},
title = {Note on the split domination number of the Cartesian product of paths},
journal = {Discussiones Mathematicae Graph Theory},
volume = {25},
year = {2005},
pages = {79-84},
zbl = {1080.05070},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1262}
}
Maciej Zwierzchowski. Note on the split domination number of the Cartesian product of paths. Discussiones Mathematicae Graph Theory, Tome 25 (2005) pp. 79-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1262/
[000] [1] R. Diestel, Graph Theory (Springer-Verlag New York, Inc., 1997).
[001] [2] M.S. Jacobson and L.F. Kinch, On the domination number of products of graphs: I, Ars Combinatoria 18 (1983) 33-44. | Zbl 0566.05050
[002] [3] V.R. Kulli and B. Janakiram, The split domination number of a graph, Graph Theory Notes of New York XXXII (1997) 16-19.