  The original Pak-Stanley labeling was defined by Pak and Stanley as a
bijective map from the set of regions of an extended Shi arrangement to the set
of parking functions. This map was later generalized to other arrangements
associated with graphs and directed multigraphs. In these more general cases
the map is no longer bijective. However, it was shown Hopkins and Perkinson and
then the first author that it is surjective to the set of the $G$-parking
functions, where $G$ is the multigraph associated with the arrangement.
  This leads to a natural question: when is the generalized Pak-Stanley map
bijective? In this paper we answer this question in the special case of central
hyperplane arrangements, i.e. the case when all the hyperplanes of the
arrangement pass through a common point.
