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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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