Koh, K. M.; Teo, C. P. The chromatic uniqueness of certain broken wheels. (English) Zbl 0752.05029 Discrete Math. 96, No. 1, 65-69 (1991). A graph \(G\) is chromatically unique if it is uniquely determined up to isomorphism by its chromatic polynomial. Let \(W(n,k)\) be the graph of order \(n\) formed by adding a new vertex adjacent to \(k\) consecutive vertices on an \((n-1)\)-cycle. It is known that \(W(n,1)\) and \(W(n,2)\) are chromatically unique for \(n\geq 4\), as are \(W(n,3)\) for \(n\geq 5\) and \(W(n,4)\) for \(n\geq 6\). However, \(W(7,5)\) is not chromatically unique. In this note the authors show that \(W(n,5)\) is chromatically unique for \(n\geq 8\). Reviewer: D.S.Archdeacon (Burlington) Cited in 10 Documents MSC: 05C15 Coloring of graphs and hypergraphs Keywords:chromatic uniqueness; chromatic polynomial; wheel; chromatically unique PDF BibTeX XML Cite \textit{K. M. Koh} and \textit{C. P. Teo}, Discrete Math. 96, No. 1, 65--69 (1991; Zbl 0752.05029) Full Text: DOI References: [1] Chao, C.Y.; Whitehead, E.G., Chromatically unique graphs, Discrete math., 27, 171-177, (1979) · Zbl 0411.05035 [2] Koh, K.M.; Teo, C.P., The chromatic uniqueness of graphs related to broken wheels, () · Zbl 0752.05029 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.