Answer to Question #171306 in Combinatorics | Number Theory for Shannon

Question

Determine the chromatic polynomial for the star S_n, where S_n is a graph with n+1 vertices consisting of n leaves all of which are adjacent to the same single vertex.

Answer 1

Chromatic Polynomial of a graph G is special function that describes the number of ways we can

achieve a proper coloring on a graph G given k colors.

Chromatic Polynomial for the star $S_n$ :

$P(S_n,k)=k(k-1)^n$