We study the average number $\mathcal{A}(G)$ of colors in the non-equivalent colorings of a graph $G$. We show some general properties of this graph invariant and determine its value for some classes of graphs. We then conjecture several lower bounds on $\mathcal{A}(G)$ and prove that these conjectures are true for specific classes of graphs such as triangulated graphs and graphs with maximum degree at most 2.

翻译：我们研究图表$G$的非等值颜色中的颜色平均值$\mathcal{A}(G) ($G) ($G$) 。 我们展示了这个图表的一些一般变量属性, 并确定其对于某些图表类别的值。 然后我们猜测$\mathcal{A}(G)$($G) 的下限, 并证明对于特定类别的图表, 如三角图表和最多最多为2的图形, 这些推测是真实的。