We show the link between the existence of perfect Lee codes and minimum dominating sets of Cartesian products of paths and cycles. From the existence of such a code we deduce the asymptotical values of the domination numbers of these graphs.
β¦ LIBER β¦
On domination number of Cartesian product of
β Scribed by Juan Liu; Xindong Zhang; Jixiang Meng
- Publisher
- Springer US
- Year
- 2010
- Tongue
- English
- Weight
- 586 KB
- Volume
- 22
- Category
- Article
- ISSN
- 1382-6905
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## Abstract A set __S__ of vertices is a determining set for a graph __G__ if every automorphism of __G__ is uniquely determined by its action on __S__. The determining number of __G__, denoted Det(__G__), is the size of a smallest determining set. This paper begins by proving that if __G__=__G__β‘β