  Tiered trees were introduced as a combinatorial object for counting
absolutely indecomposable representation of certain quivers and torus orbit of
certain homogeneous variety. In this paper, we define a bijection between the
set of parallelogram polyominoes and graphical parking functions. Moreover, we
defined the space $\mathcal{S}_{G}$ for complete tiered graphs and described
tiered graphs in terms of Whitney's operations.
