ABSTRACT
In this chapter, we continue our study of domination, focusing on domination of Cartesian products. When trying to compute a fixed invariant of graphs, it is often useful to know that the graphs being considered are from a known class. The structure of the graphs in that class can be used to deduce certain bounds for the invariant. For example, the vertex independence number of a general graph G of order n can assume any value from 1 to n, but if only bipartite graphs are being considered, then the independence number will be at least n/2. In a similar way, the knowledge that a graph is the Cartesian product of two nontrivial graphs can be used to conclude certain things about the domination number.
