Suppose $c(G,u)$ is chromatic polynomial of connected simple graph $G$. We know that $|c(G,-1)|$, as Stanley proved, is the total number of directed graph on $G$, without any cycle. Also, we know some other graphical representations of the value of $c(G,u)$.
1) Do we have any graphical representation for $|c(G,2)|$?
2) Do we have any graphical representation for the multiplicity of $2$ as a root of $c(G,u)$?
I found some graphical representation for these values, but I didn't prove them yet.
Thanks for any helpful answer and good references.