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The chromaticity of wheels. (English) Zbl 0547.05032
A graph G is said to be chromatically unique, if \(P(H,\lambda)=P(G,\lambda)\) implies that H is isomorphic to G, where P(G,\(\lambda)\) denotes the chromatic polynomial of G. In this paper it is proved that the wheel \(W_{n+1}\) is chromatically unique if n is even but \(W_ 8\) is not chromatically unique. Since \(W_ 6\) is also not chromatically unique the following conjecture is made: The wheel \(W_{n+1}\) is not chromatically unique for odd \(n\geq 9\).
Reviewer: I.Tomescu

05C15 Coloring of graphs and hypergraphs
Full Text: DOI
[1] Chao, C.Y.; Whitehead, E.G., On chromatic equivalence of graphs, (), 121-131
[2] Chao, C.Y.; Whitehead, E.G., Chromatically unique graphs, Discrete math., 27, 171-177, (1979) · Zbl 0411.05035
[3] Tutte, W.T., On chromatic polynomials and the Golden ratio, J. combin. theory, 9, 289-296, (1970) · Zbl 0209.55001
[4] Harary, F., Graph theory, (1969), Addison-Wesley Reading, MA · Zbl 0797.05064
[5] Read, R.C., An introduction to chromatic polynomials, J. combin. theory, 4, 52-71, (1968) · Zbl 0173.26203
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