%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