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On the domination number of products of graphs. I. (English) Zbl 0566.05050

In this paper we consider a problem of Cockayne, to determine a relationship between the domination number of a graph product versus the product of the domination numbers. For some very special cases we show, in fact, that \[ (1)\quad \sigma (G\times H)\geq \sigma (G)\cdot \sigma (H), \] where \(\sigma\) (F) is the domination number of the graph F. This paper supports the conjecture that statement (1) is true for all graphs G and H.

MSC:

05C99 Graph theory
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