An dimensional De Bruijn graph of symbols is a directed graph with vertices and the edges defined as below.

The vertices consist of all possible way combinations of the symbols. If we have the symbols then the set of vertices is:

.

If one of the vertices can be expressed by shifting all symbols by one place to the left and adding a new symbol at the end of another vertex, then the later has a directed edge to the former vertex. Thus the set of (directed) edges is:

Note: 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.