de Bruijn Graph
---------------
A graph whose nodes are sequences of symbols from some 
Alphabet and whose edges indicate the sequences which 
might overlap. 

References 

Golomb, S. W. Shift Register Sequences. San Francisco, 
CA: Holden-Day, 1967. 

Ralston, A. ``de Bruijn Sequences--A Model Example of 
the Interaction of Discrete Mathematics and
Computer Science.'' Math. Mag. 55, 131-143, 1982. 


de Bruijn Sequence 
------------------
The shortest sequence such that every string of length n
on the Alphabet a occurs as a contiguous subrange of the 
sequence described by a. Every de Bruijn sequence
corresponds to an Eulerian Cycle on a de Bruijn Graph. 
Surprisingly, it turns out that the lexicographic sequence 
of Lyndon Words of lengths Divisible by n gives the
lexicographically smallest de Bruijn sequence (Ruskey). 

References 

Ruskey, F. ``Information on Necklaces, Lyndon Words, de Bruijn
Sequences.''
http://sue.csc.uvic.ca/~cos/inf/neck/NecklaceInfo.html.