The dissertation is a study of three products---the Cartesian, the hierarchical (rooted) and the (generalized) hierarchical product. We discuss whether it is possible to uniquely represent every simple finite graph as a hierarchical product of graphs that can not be factorized with respect to the hierarchical product. As the hierarchical product is a generalization of the Cartesian product, we first explore the problem for the latter. We deal with the question of domination of both products. We derive some bounds for the domination number of the Cartesian and the hierarchical product and present some results in relation to Vizing's conjecture.
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