# zbMATH — the first resource for mathematics

Cutpoints and the chromatic polynomial. (English) Zbl 0551.05041
From the authors’ abstract: ”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 $$(\lambda -1)^ 2$$. We apply this theorem to obtain some chromatic equivalence and uniqueness results.”