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On the uniqueness of the chromatic polynomials of generalized wheel graphs. (Chinese. English summary) Zbl 0774.05038
Summary: We prove that the generalized wheel graph \(\theta_{n,k}\) is chromatically unique if \(k\geq 0\) and \(n\geq 4\) is even. Meanwhile, it also has been proved that for a graph \(G\) we have \(P_ \lambda(G)=\lambda\cdots(\lambda-q+1)(\lambda-q)^{n-q}\) if and only if \(G\) is a \(q\)-tree on \(n\) vertices.

MSC:
05C15 Coloring of graphs and hypergraphs
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