Chromaticity of a family of K4-homeomorph with Girth 9

Abstract

Abstract. 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 investigate the chromaticity of one family of K 4 -homeomorph which has girth 9, and give sufficient and necessary condition for the graph in the family to be chromatically unique.