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The chromaticity of wheels with a missing spoke. (English) Zbl 0712.05025
Let G be a finite undirected graph without loops or multiple edges, and let P(G,$$\lambda$$) denote its chromatic polynomial. A graph G is said to be chromatically unique if every graph H with $$P(G,\lambda)=P(H,\lambda)$$ is isomorphic with G. A wheel $$W_{n+1}$$ is obtained by taking the join of $$K_ 1$$ and a cycle $$C_ n$$ on n vertices. The graph obtained from $$W_ n$$ by deleting one edge which joins $$K_ 1$$ and a vertex of $$C_ n$$ is denoted by $$U_{n+1}$$. $$U_ 4$$, $$U_ 5$$ and $$U_ 6$$ are chromatically unique graphs but $$U_ 7$$ is not. It is proved that $$U_{n+1}$$ is chromatically unique if $$n\geq 3$$ is odd.
Reviewer: U.Baumann

##### MSC:
 05C15 Coloring of graphs and hypergraphs
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