Cutpoints and the chromatic polynomial

@article{Whitehead1984CutpointsAT,
  title={Cutpoints and the chromatic polynomial},
  author={Earl Glen Whitehead and Lian-Chang Zhao},
  journal={Journal of Graph Theory},
  year={1984},
  volume={8},
  pages={371-377}
}
We prove that the multiplicity of the root 1 in the chromatic polynomial of a simple graph G is equal to the number of nontrivial blocks in G. In particular, a connected simple graph G has a cutpoint if and only if its chromatic polynomial is divisible by (A 1)'. We apply this theorem to obtain some chromatic equivalence and uniqueness results.