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Unformatted text preview: king of these vertices as the
vertices of a square, those of the order N = 3 de Bruijn graph can be viewed as
vertices of a cube, those of the order N = 4 de Bruijn graph as the vertices of
a hypercube, and so on.
For each de Bruijn graph over a binary alphabet, each vertex is the terminal 65 2.5. FASTER CONVERGENCE: DE BRUIJN SEQUENCES
00 1 0 0 0 1 10 00 01 8 7 2 6 10 11 01 5 11
3 1 4 1 Figure 2.32: Left: An N = 2 de Bruijn graph. Right: An N = 3 de Bruijn
point of two edges, and each vertex is the initial point of two edges. Speciﬁcally,
the vertex ab is the terminal point of the edges
a b0 −→ ab a and b1 −→ ab and the initial point of the edges
0 ab −→ 0a 1 and ab −→ 1a Some authors append the next entry on the right instead of on the left. We
append the new entries on the left so the order of the strings is the order of the
corresponding composition of functions, in turn the address of the region which
is the result of applying the transformations in that order.
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