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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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