Domination In The Cross Product Of Digraphs

In many papers, the relation between the domination number of a product of graphs and the product of domination numbers of factors is studied. Here we investigate this problem for domination and total domination numbers in the cross product of digraphs. We give analogues of known results for graphs, and we also present new results for digraphs with sources. Using these results we find domination (total domination) numbers for some classes of digraphs. This is a preprint of an article accepted for publication in Ars Combinatoria c ©2010 (copyright owner as specified in the journal).