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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
##### Keywords:
wheel; chromatically unique graphs; chromatic polynomial
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##### References:
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