Whitehead, Earl Glen jun.; Zhao, Lian-Chang Cutpoints and the chromatic polynomial. (English) Zbl 0551.05041 J. Graph Theory 8, 371-377 (1984). 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 Cited in 2 ReviewsCited in 30 Documents MSC: 05C15 Coloring of graphs and hypergraphs 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) Keywords:chromatic polynomial; cutpoint; chromatic equivalence PDF BibTeX XML Cite \textit{E. G. Whitehead jun.} and \textit{L.-C. Zhao}, J. Graph Theory 8, 371--377 (1984; Zbl 0551.05041) Full Text: DOI References: [1] and , On chromatic equivalence of graphs. In Theory and Applications of Graphs, Lecture Notes in Math. 642, and , Eds. Springer, New York (1978), pp. 121–131. [2] Crapo, J. Combinatorial Theory 2 pp 406– (1967) · Zbl 0149.25901 [3] Characterization of a polygonal graph by means of its chromatic polynomial. In Proceedings of the Fourth Southeastern Conference on Combinatorics, Graph Theory, and Computing. Utilitas, Winnipeg (1973), pp. 275–278. [4] Giudici, Some new families of chromatically unique graphs · Zbl 0567.05023 [5] Halin, J. Combinatorial Theory 7 pp 150– (1969) [6] Graph Theory. Addison-Wesley, Reading, MA (1969). [7] Read, J. Combinatorial Theory 4 pp 52– (1968) · Zbl 0165.32802 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.