Geodesic
Note on the split domination number of the Cartesian product of paths
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 79-84

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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.
Keywords: domination number, split domination number, Cartesian product of graphs 
Zwierzchowski, Maciej. Note on the split domination number of the Cartesian product of paths. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 79-84. http://geodesic.mathdoc.fr/item/DMGT_2005_25_1-2_a8/
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[1] R. Diestel, Graph Theory (Springer-Verlag New York, Inc., 1997).

[2] M.S. Jacobson and L.F. Kinch, On the domination number of products of graphs: I, Ars Combinatoria 18 (1983) 33-44.

[3] V.R. Kulli and B. Janakiram, The split domination number of a graph, Graph Theory Notes of New York XXXII (1997) 16-19.