Graphical Stirling number (${\left\{\begin{array}{c}n\\ k\end{array}\right\}}_G$)

The graphical Stirling number ${\left\{\begin{array}{c}n\\ k\end{array}\right\}}_G$ counts partitions of the vertices of a graph $G$ into $k$ nonempty independent sets. Equivalently, it counts proper colourings with $k$ unlabeled nonempty colour classes.