CHROMATIC EQUIVALENCE OF A FAMILY OF K4-HOMEOMORPHS WITH GIRTH 9
Roslan Hasni · International Journal of Pure and Apllied Mathematics · 2013
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 K 4 -homeomorph is a subdivision of the complete graph K 4 .In this paper, we determine when two K 4 -homeomorphs of the form K 4 (2, 3, 4, d, e, f ) and K 4 (1, 2, 6, d ′ , e ′ , f ′ ) are chromatically equivalent.The result obtained can be extended in the study of chromatic equivalence classes of K 4 (2, 3, 4, d, e, f ) and chromatic uniqueness of K 4 -homeomorphs with girth 9.