The chromaticity of certain graphs with five triangles. (English) Zbl 0787.05040

Li, Nian-Zu; Whitehead, Earl Glen jun.

Discrete Math. 122, No. 1-3, 365-372 (1993).

Summary: Let \(W(n,k)\) denote the graph of order \(n\) obtained from the wheel \(W_ n\) by deleting all but \(k\) consecutive spokes. We study the chromaticity of graphs which share certain properties of \(W(n,6)\) which can be obtained from the coefficients of the chromatic polynomial of \(W(n,6)\). In particular, we prove that \(W(n,6)\) is chromatically unique for all integers \(n\geq 8\). We also obtain two additional families of chromatically unique graphs.

MSC:

05C15

Coloring of graphs and hypergraphs

Keywords:

wheel; chromaticity; chromatic polynomial; chromatically unique graphs

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