  A coloring of a graph is an assignment of colors to its vertices such that
adjacent vertices have different colors. Two colorings are equivalent if they
induce the same partition of the vertex set into color classes. Let
$\mathcal{A}(G)$ be the average number of colors in the non-equivalent
colorings of a graph $G$. We give a general upper bound on $\mathcal{A}(G)$
that is valid for all graphs $G$ and a more precise one for graphs $G$ of order
$n$ and maximum degree $\Delta(G)\in \{1,2,n-2\}$.
