De Bruijn digraph

The vertices of the de Bruijn digraph $B(n,m)$ are all possible words of length $m-1$ chosen from an alphabet of size $n$.

$B(n,m)$ has $n^\{m\}$ edges consisting of each possible word of length $m$ from an alphabet of size $n$. The edge $a\_1a\_2dots\; a\_n$ connects the vertex $a\_1a\_2dots\; a\_\{n-1\}$ to the vertex $a\_2a\_3dots\; a\_n$.

For example, $B(2,4)$ could be drawn as:

Notice that an Euler cycle on $B(n,m)$ represents a shortest sequence of characters from an alphabet of size $n$ that includes every possible subsequence of $m$ characters. For example, the sequence $000011110010101000$ includes all 4-bit subsequences. Any de Bruijn digraph must have an Euler cycle, since each vertex has in degree and out degree of $m$.