zbMATH — the first resource for mathematics

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