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 $\Delta(G)\in \{1,2,n-2\}$.

翻译：图形的颜色是向它的顶端分配颜色, 使相邻的顶端有不同的颜色。 两个颜色等值, 如果它们将顶端对颜色类别进行相同的分隔。 请将$\ mathcal{A}( G)$作为图中非等值的颜色的平均数量 $G$。 我们给所有图形都有效的$\ mathcal{A}( G)$上下一个总上限, 对所有图形都有效 $G$, 并且给图表中 $G$ 和 $\ Delta( G)\ $ 1, 2, n-2 $ 中一个更精确的值 $G$和 $Delta( G)\ $ 1, 2, $。