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The chromaticity of wheels with a missing spoke. II. (English) Zbl 0838.05052
Summary: In the previous paper [ibid. 82, No. 2, 209-212 (1990; Zbl 0712.05025)], it was shown that the graph $$U_{n+ 1}$$ obtained from the wheel $$W_{n+ 1}$$ by deleting a spoke is uniquely determined by its chromatic polynomial if $$n\geq 3$$ is odd. In this paper, we show that the result is also true for even $$n\geq 4$$ except when $$n= 6$$ in which case, the graph $$W$$ given in the paper is the only graph having the same chromatic polynomial as that of $$U_7$$. The relevant tool is the notion of nearly uniquely colorable graph.

MSC:
 05C15 Coloring of graphs and hypergraphs
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References:
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