Discussiones Mathematicae Graph Theory 25(12) (2005)
7984
doi: 10.7151/dmgt.1262
NOTE ON THE SPLIT DOMINATION NUMBER OF THE CARTESIAN PRODUCT OF PATHS
Maciej Zwierzchowski
Institute of Mathematics
Technical University of Szczecin
Al. Piastów 48/49, 70310 Szczecin, Poland
email: mzwierz@ps.pl
Abstract
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 P_{m}□ P_{n} was studied. The split domination number of
P_{2}□ P_{n} is calculated, and we give good estimates for the split
domination number of P_{m}□ P_{n} expressed in terms of its domination
number.
Keywords: domination number, split domination number,
Cartesian product of graphs.
2000 Mathematics Subject Classification: 05C69.
References
[1] 
R. Diestel, Graph Theory (SpringerVerlag 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) 3344.

[3] 
V.R. Kulli and B. Janakiram, The split domination
number of a graph, Graph Theory Notes of New York XXXII (1997) 1619.

Received 31 October 2003
Revised 12 May 2004