  Kreweras proved that the reversed sum enumerator for parking functions of
length $n$ is equal to the inversion enumerator for labeled trees on $n+1$
vertices. Recently, Perkinson, Yang, and Yu gave a bijective proof of this
equality that moreover generalizes to graphical parking functions. Using a
depth-first search variant of Dhar's burning algorithm they proved that the
codegree enumerator for $G$-parking functions equals the $\kappa$-number
enumerator for spanning trees of $G$. The $\kappa$-number is a kind of
generalized tree inversion number originally defined by Gessel. We extend the
work of Perkinson-Yang-Yu to what are referred to as "generalized parking
functions" in the literature, but which we prefer to call vector parking
functions because they depend on a choice of vector $\mathbf{x} \in
\mathbb{N}^n$. Specifically, we give an expression for the reversed sum
enumerator for $\mathbf{x}$-parking functions in terms of inversions in rooted
plane trees with respect to certain admissible vertex orders. Along the way we
clarify the relationship between graphical and vector parking functions.
