Properties
- If then the condition for any two vertices forming an edge holds vacuously, and hence all the vertices are connected forming a total of edges.
- Each vertex has exactly incoming and outgoing edges.
- Each -dimensional De Bruijn graph is the line digraph of the -dimensional De Bruijn graph with the same set of symbols.
- Each De Bruijn graph is Eulerian and Hamiltonian. The Euler cycles and Hamiltonian cycles of these graphs (equivalent to each other via the line graph construction) are De Bruijn sequences.
The line graph construction of the three smallest binary De Bruijn graphs is depicted below. As can be seen in the illustration, each vertex of the -dimensional De Bruijn graph corresponds to an edge of the -dimensional De Bruijn graph, and each edge in the -dimensional De Bruijn graph corresponds to a two-edge path in the -dimensional De Bruijn graph.
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