On chromatic equivalence of a pair of K4-homeomorphs

Abstract

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.