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Discussiones Mathematicae Graph Theory 24(3) (2004) 389-402
DOI: https://doi.org/10.7151/dmgt.1238

ON DOMINATING THE CARTESIAN PRODUCT OF A GRAPH AND K₂

Bert L. Hartnell Saint Mary's University Halifax, Nova Scotia, Canada B3H 3C3 e-mail: drall@herky.furman.edu

Douglas F. Rall Furman University Greenville, SC 29613 USA e-mail: bert.hartnell@smu.ca

Abstract

In this paper we consider the Cartesian product of an arbitrary graph and a complete graph of order two. Although an upper and lower bound for the domination number of this product follow easily from known results, we are interested in the graphs that actually attain these bounds. In each case, we provide an infinite class of graphs to show that the bound is sharp. The graphs that achieve the lower bound are of particular interest given the special nature of their dominating sets and are investigated further.

Keywords: domination; 2-packing, Cartesian product.

2000 Mathematics Subject Classification: 05C69.

References

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Received 20 January 2003
Revised 30 March 2004