%0 Journal Article %T A new result on chromaticity of K4-homoemorphs with girth 9 %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Karim, N.S.A. %A Hasni, R. %A Lau, G.C. %D 2017 %\ 04/01/2017 %V 43 %N 2 %P 319-336 %! A new result on chromaticity of K4-homoemorphs with girth 9 %K Chromatic polynomial %K chromatically unique %K $K_4$-homeomorphs %R %X For a graph $G$, let $P(G,lambda)$ denote the chromatic polynomial of $G$. Two graphs $G$ and $H$ are chromatically equivalent if they share the same chromatic polynomial. A graph $G$ is chromatically unique if any graph chromatically equivalent to $G$ is isomorphic to $G$. A $K_4$-homeomorph is a subdivision of the complete graph $K_4$. In this paper, we determine a family of chromatically unique $K_4$-homeomorphs which have girth 9 and has exactly one path of length 1, and give sufficient and necessary condition for the graphs in this family to be chromatically unique. %U http://bims.iranjournals.ir/article_934_939a971a7355485402466c756b6fb1a9.pdf