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On chromatic equivalence of a pair of K4-homeomorphs

Catada-Ghimire S., Roslan H., Peng Y. H.

Opuscula Mathematica

2010

Vol. 30, no. 2

123-131

Let P(G, λ) be the chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically euqivalent, denoted G ∼ H, if P(G, λ) = P(H, λ). We write [G] = {H/H ∼ G}. If [G] = {G}, then G is said to be chromatically unique. In this paper, we discuss a chromatically equivalent pair of graphs in one family of K4-homeomorphs, K4(1, 2, 8, d, e, f). The obtained result can be extended in the study of chromatic equivalence classes of K4(1, 2, 8, d, e, f) and chromatic uniqueness of K4-homeomorphs with girth 11.