CID 2003 Abstracts - Colourings, Independence and Domination

52 abstracts
ON THE SPLIT DOMINATION NUMBER
OF THE CARTESIAN PRODUCT OF PATHS
Maciej Zwierzchowski
Technical University of Szczecin, Poland
Let D be a dominating set of G. If the subgraph induced by the subset
V (G) − D is disconnected, then D is called a split dominating set of G. By
γ s (G) we mean the cardinality of the smallest split dominating set of G and
we call it the split domination number of G. The concept of split domination
comes from [2].
In this paper we discuss the split domination number with respect to the
Cartesian product of paths. Motivation of this problem comes from [1], where
was study the domination number of P m ×P n . We calculate the γ s (P 2 ×P n ) and
estimate the γ s (P m × P n ) using the domination number of P m × P n . Further,
we discuss a γ s (P m × P n ) with respect to large integer m and n.
Keywords: domination number, split domination number, Cartesian product
of graphs.
AMS Subject Classification: 05C69.
References
[1] M.S. Jacobson, L.F. Kinch, On the domination number of products of
graphs: I, Ars Combinatoria 18 (1983) 33-44.
[2] V.R. Kulli, B. Janakiram, The split domination number of a graph, Graph
Theory of New York XXXII (1997) 16-19.