ChromaticPolynomial

ChromaticPolynomial[g, k] gives the chromatic polynomial of the graph g.

ChromaticPolynomial[{v -> w, ...}, k] uses rules to specify the graph g.

Examples

Chromatic polynomial of a complete graph:

ChromaticPolynomial[CompleteGraph[4], k]
(* k (k - 1) (k - 2) (k - 3) *)

Chromatic polynomial of a cycle:

ChromaticPolynomial[CycleGraph[5], k]
(* (k - 1)^5 + (k - 1) *)

Please visit the official Wolfram Language Reference for more details.