§ The chromatic polynomial (TODO)

I've been on a combinatorics binge lately, so I'm collecting cool facts about the chromatic polynomial. We first define the chromatic function of a graph, which is a generating function:
f[G](x)≡number of ways to color G with x colors⋅xn f[G](x) \equiv \texttt{number of ways to color $G$ with $x$ colors} \cdot x^n
If we have a single vertex K1K_1, then f[K1](x)=nxnf[K_1](x) = n x^n, since we can color the single vertex with the nn colors we have.

§ Composition of chromatic funcions of smaller graphs

§ The chromatic function is a polynomial