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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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