I am asked the following:
Let n be a positive integer at least 3.
The wheel W_n is the graph obtained by taking the cycle C_n, placing an additional vertex at the center, and joining it to each of the other n vertices on the rim using n more edges (spokes).
Find the chromatic polynomial for W_n.
I know that the form of a chromatic polynomial of a wheel graph looks like: ${P_w}_n(x)= x((x-2)^{n-1} - (-1)^n(x-2)) $ The equation above doesn't take into acount the "vertex at the center" as asked in the question. I am confused on how to proceeding with this problem in order to find the chromatic polynomial $W_n$ any help or guidance is welcome.