Discussiones Mathematicae Graph Theory 31(1) (2011) 5-23
doi: 10.7151/dmgt.1526

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PAIRED DOMINATION IN PRISMS OF GRAPHS

Christina M. Mynhardt and Mark Schurch

Department of Mathematics and Statistics
University of Victoria
P.O. Box 3060 STN CSC
Victoria, BC, Canada V8W 3R4
e-mail: mynhardt@math.uvic.ca, mschurch@math.uvic.ca

Abstract

The paired domination number γpr(G) of a graph G is the smallest cardinality of a dominating set S of G such that áSñ has a perfect matching. The generalized prisms πG of G are the graphs obtained by joining the vertices of two disjoint copies of G by |V(G)| independent edges. We provide characterizations of the following three classes of graphs: γpr(πG) = 2γpr(G) for all πG; γpr(K2□G) = 2γpr(G); γpr(K2□G) = γpr(G).

Keywords: domination, paired domination, prism of a graph, Cartesian product.

2010 Mathematics Subject Classification: 05C69.

References

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Received 29 January 2009
Revised 27 July 2009
Accepted 27 July 2009