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Discussiones Mathematicae Graph Theory 21(1) (2001) 303-310
DOI: https://doi.org/10.7151/dmgt.1152

A NOTE ON DOMINATION PARAMETERS OF THE CONJUNCTION OF TWO SPECIAL GRAPHS

Maciej Zwierzchowski

Institute of Mathematics
University of Technology of Szczecin
al. Piastów 48/49, 70-310 Szczecin, Poland
e-mail: mzwierz@arcadia.tuniv.szczecin.pl

Abstract

A dominating set D of G is called a split dominating set of G if the subgraph induced by the subset V(G)−D is disconnected. The cardinality of a minimum split dominating set is called the minimum split domination number of G. Such subset and such number was introduced in [4]. In [2], [3] the authors estimated the domination number of products of graphs. More precisely, they were study products of paths. Inspired by those results we give another estimation of the domination number of the conjunction (the cross product) P_n∧G. The split domination number of P_n∧G also is determined. To estimate this number we use the minimum connected domination number γ_c(G).

Keywords: domination parameters, conjunction of graphs.

2000 Mathematics Subject Classification: 05C69.

References

[1]	R. Diestel, Graph Theory (Springer-Verlag, New York, Inc., 1997).
[2]	S. Gravier and A. Khelladi, On the domination number of cross products of graphs, Discrete Math. 145 (1995) 273-277, doi: 10.1016/0012-365X(95)00091-A.
[3]	M.S. Jacobson and L.F. Kinch, On the domination number of products of graphs: I, Ars Combin. 18 (1983) 33-44.
[4]	V.R. Kulli and B. Janakiram, The split domination number of a graph, Graph Theory Notes of New York XXXII (1997) 16-19.
[5]	E. Sampathkumar and H.B. Walikar, The connected domination number of graph, J. Math. Phy. Sci. 13 (1979) 607-613.

Received 28 March 2001
Revised 7 September 2001