Springer and the Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401A new result on chromaticity of K4-homoemorphs with girth 9319336934ENN.S.A.KarimDepartment of Mathematics, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris,
35900 Tanjong Malim, Perak, Malaysia.R.HasniSchool of Informatics and Applied Mathematics,
University Malaysia Terengganu,
21030 Kuala Terengganu, Terengganu, Malaysia.G.C.LauFaculty of Computer and Mathematical Sciences,
University Teknologi MARA (Segamat Campus)
85000 Segamat, Johor, Malaysia.Journal Article20150324For 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.http://bims.iranjournals.ir/article_934_939a971a7355485402466c756b6fb1a9.pdf