## 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

### Keywords:

domination number; graph product