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On the chromatic uniqueness of the graph $$W(n,n-2,k)$$. (English) Zbl 0857.05039
For integers $$n\geq 4$$ and $$k\geq 1$$, $$W(n,n-2,k)$$ denotes a graph constructed in the following manner: Take a wheel $$W_n$$ of order $$n$$ (i.e. $$W_n$$ consists of a cycle $$C$$ of length $$n-1$$ and a vertex $$v$$ incident to all vertices of $$C$$), delete an edge between $$v$$ and some vertex $$u$$ of $$C$$, and replace $$u$$ by $$k$$ independent vertices $$u_1,\dots,u_k$$ such that the neighbourhood of each $$u_i$$ consists of the two neighbours of $$u$$ in $$C$$. The authors prove that $$W(n,n-2,k)$$ is chromatically unique for each even $$n\geq6$$ and each $$k\geq1$$, i.e. each graph having the same chromatic polynomial as $$W(n,n-2,k)$$ is isomorphic to $$W(n,n-2,k)$$.
Reviewer: A.Huck (Hannover)

##### MSC:
 05C15 Coloring of graphs and hypergraphs
##### Keywords:
chromatic uniqueness; wheel; chromatic polynomial
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##### References:
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