CHROMATIC EQUIVALENCE OF $K_4$-HOMEOMORPHS WITH GIRTH 9
Roslan Hasni, Ali Hasan Ahmad, Faridah Mustapha · International Journal of Pure and Apllied Mathematics · 2012
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 K4- homeomorphs 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.