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 $a_1a_2\dots a_n$ connects the vertex $a_1a_2\dots a_{n-1}$ to the vertex $a_2a_3\dots a_n$

For example, $B(2,4)$ could be drawn as: $$\xymatrix{ & 000 \ar@(ur,ul)[]_{0000} \ar[dr]^{0001} & \\ 100 \ar[ur]^{1000} \ar[rr]^{1001} & & 001 \ar[dl]^{0010} \ar[ddd]^{0011}\\ & 010 \ar[ul]^{0100} \ar@(ur,dr)[d]^{0101} & \\ & 101 \ar[dr]^{1011} \ar@(dl,ul)[u]^{1010} & \\ 110 \ar[uuu]^{1100} \ar[ur]^{1101} & & 011 \ar[ll]_{0110} \ar[dl]^{0111}\\ & 111 \ar@(dl,dr)[]_{1111} \ar[ul]^{1110} & }$$

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 $n$