The chromatic polynomial of graph G is the function PG(k) that gives the number of ways to color the vertices of G using k colors, such that no two adjacent vertices have the same color.
(a) If L is a path (linear graph) with vertices, show that Pk(u) = k(k - 1)^(n-1).
(b) Let Cn be the cyclic graph with n vertices. Find Pcs(k).
(c) Show that for n > 3, Pcn(k) satisfies the recurrence: Pcn(k) = k(k - 1)^(n-1) Pcn-1(k).