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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

MSC:
05C15 Coloring of graphs and hypergraphs
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References:
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