Discussiones Mathematicae Graph Theory 25(1-2) (2005) 79-84
doi: 10.7151/dmgt.1262

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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, 70-310 Szczecin, Poland

e-mail: 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 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.

2000 Mathematics Subject Classification: 05C69.

References

[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.

Received 31 October 2003
Revised 12 May 2004