Editing Chromatic polynomial (section)

===Chromatic equivalence===
[[File:Chromatically equivalent graphs.svg|thumb|right|250px|{{center|The three graphs with a chromatic polynomial equal to <math>(x-2)(x-1)^3x</math>.}}]]

Two graphs are said to be ''chromatically equivalent'' if they have the same chromatic polynomial. Isomorphic graphs have the same chromatic polynomial, but non-isomorphic graphs can be chromatically equivalent. For example, all trees on ''n'' vertices have the same chromatic polynomial.
In particular, <math>(x-1)^3x</math> is the chromatic polynomial of both the [[claw (graph theory)|claw graph]] and the [[path graph]] on 4 vertices.

A graph is ''chromatically unique'' if it is determined by its chromatic polynomial, up to isomorphism. In other words, ''G'' is chromatically unique, then <math>P(G, x) = P(H, x)</math> would imply that ''G'' and ''H'' are isomorphic.
All [[cycle graph]]s are chromatically unique.<ref>{{harvtxt|Chao|Whitehead|1978}}</ref>