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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.”
Reviewer: R.C.Read

05C15 Coloring of graphs and hypergraphs
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
Full Text: DOI
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