  Plunnecke's inequality is the standard tool to obtain estimates on the
cardinality of sumsets and has many applications in additive combinatorics. We
present a new proof. The main novelty is that the proof is completed with no
reference to Menger's theorem or Cartesian products of graphs. We also
investigate the sharpness of the inequality and show that it can be sharp for
arbitrarily long, but not for infinite commutative graphs. A key step in our
investigation is the construction of arbitrarily long regular commutative
graphs. Lastly we prove a necessary condition for the inequality to be
attained.
