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Motivated by the work on the domination number of directed de Bruijn graphsand some of its generalizations, in this paper we introduce a naturalgeneralization of de Bruijn graphs (directed and undirected), namely$t$-constrained de Bruijn graphs, where $t$ is a positive integer, and thenstudy the domination number of these graphs.  Within the definition of $t$-constrained de Bruijn graphs, de Bruijn andKautz graphs correspond to 1-constrained and 2-constrained de Bruijn graphs,respectively. This generalization inherits many structural properties of deBruijn graphs and may have similar applications in interconnection networks orbioinformatics.  We establish upper and lower bounds for the domination number on$t$-constrained de Bruijn graphs both in the directed and in the undirectedcase. These bounds are often very close and in some cases we are able to findthe exact value.

On the domination number of $t$-constrained de Bruijn graphs