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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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##### References:
 [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] Farrell, E.J., On chromatic coefficients, Discrete math., 29, 257-264, (1980) · Zbl 0443.05041 [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 [6] Read, R.C., A note on the chromatic uniqueness of W10, Discrete math., 69, 317, (1988) · Zbl 0639.05019 [7] Whitehead, E.G.; Zhao, L.-C., Cutpoints and the chromatic polynomial, J. graph theory, 8, 371-377, (1984) · Zbl 0551.05041 [8] Xu, S.-J.; Li, N.-Z., The chromaticity of wheels, Discrete math., 51, 207-212, (1984) · Zbl 0547.05032
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