Domination In the Cross Product of Digraphs

Abstract

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.