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Chromatic equivalence classes of certain generalized polygon trees. III. (English) Zbl 1021.05035
Summary: Let \(P(G)\) denote the chromatic polynomial of a graph \(G\). Two graphs \(G\) and \(H\) are chromatically equivalent, if \(P(G)=P(H)\). A set of graphs \({\mathcal S}\) is called a chromatic equivalence class if any graph \(H\) that is chromatically equivalent with a graph \(G\) in \({\mathcal S}\), also belongs to \({\mathcal S}\). In Part I Y.-H. Peng et al. [Discrete Math. 172, 103-114 (1997; Zbl 0883.05058)] studied the chromatic equivalence classes of certain generalized polygon trees. In this Part III, we continue that study and present a solution to Problem 2 in K. M. Koh and K. L. Teo [Discrete Math. 172, 59-78 (1997; Zbl 0879.05031)]. Part II has been submitted for publication.

MSC:
05C15 Coloring of graphs and hypergraphs
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