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The chromatic uniqueness of certain broken wheels. (English) Zbl 0752.05029
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 \(n\geq 8\).

MSC:
05C15 Coloring of graphs and hypergraphs
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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
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