  Given an undirected graph $G=(V,E)$, and a designated vertex $q\in V$, the
notion of a $G$-parking function (with respect to $q$) was independently
developed and studied by various authors, and has recently gained renewed
attention. This notion generalizes the classical notion of a parking function
associated with the complete graph. In this work, we study properties of {\em
maximum} $G$-parking functions and provide a new bijection between them and the
set of spanning trees of $G$ with no broken circuit. As a case study, we
specialize some of our results to the graph corresponding to the discrete
$n$-cube $Q_n$. We present the article in an expository self-contained form,
since we found the combinatorial aspects of $G$-parking functions somewhat
scattered in the literature, typically treated in conjunction with sandpile
models and closely related chip-firing games.
