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On domination number of Cartesian product of

✍ 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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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.

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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‹