A new result on chromaticity of K4-homoemorphs with girth 9

Document Type: Research Paper

Authors

1 Department of Mathematics‎, ‎Faculty of Science and Mathematics‎, ‎Universiti Pendidikan Sultan Idris‎, ‎35900 Tanjong Malim‎, ‎Perak‎, ‎Malaysia.

2 School of Informatics and Applied Mathematics‎, ‎University Malaysia Terengganu‎, ‎21030 Kuala Terengganu‎, ‎Terengganu‎, ‎Malaysia.

3 Faculty of Computer and Mathematical Sciences‎, ‎University Teknologi MARA (Segamat Campus) ‎85000 Segamat‎, ‎Johor‎, ‎Malaysia.

Abstract

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.

Keywords

Main Subjects


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Volume 43, Issue 2
March and April 2017
Pages 319-336
  • Receive Date: 24 March 2015
  • Revise Date: 17 November 2015
  • Accept Date: 17 November 2015