Chromatic Equivalence of K 4 - Homeomorphs with Girth 9

For a graph G, let P (G,λ) denote the chromatic polynomial of G. Two graphs G and H are chromatically equivalent (or simply χ−equivalent), denoted by G ∼ H, if P (G,λ) = P (H,λ). A graph G is chromatically unique (or simply χ−unique) if for any graph H such as H ∼ G, we have H ∼= G, i.e, H is isomorphic to G. A K4-homeomorph is a subdivision of the complete graph K4. In this paper, we discuss a pair of chromatically equivalent of K4homeomorphs with girth 9, that is, K4(1, 3, 5, d, e, f) and K4(1, 3, 5, d , e, f ). As a result, we obtain two infinite chromatically equivalent non-isomorphic K4-homeomorphs. AMS Subject Classification: 05C15