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{\bf Dustin A. Cartwright, Mar\'ia Ang\'elica Cueto and Enrique A. Tobis}
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{\bf The Maximum Independent Sets of de Bruijn Graphs of Diameter  3}
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  The nodes of the de Bruijn graph $B(d,3)$ consist of all strings of
  length $3$, taken from an alphabet of size $d$, with edges between
  words which are distinct substrings of a word of length~$4$.  We
  give an inductive characterization of the maximum independent sets
  of the de Bruijn graphs $B(d,3)$ and for the de Bruijn graph of
  diameter three with loops removed, for arbitrary alphabet size.  We
  derive a recurrence relation and an exponential generating function
  for their number. This recurrence allows us to construct
  exponentially many comma-free codes of length~3 with maximal
  cardinality.

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