Hasni, Roslan (2009) *An attempt to classify bipartite graphs by their chromatic Polynomial.* Project Report. Universiti Sains Malaysia. (Submitted)

## Abstract

For the purpose of tackling the four-colour problem, Birkhoff (1912) introduced the chromatic polynomial of a map, denoted by P(M,A), which is a number of proper Acolouring of a map M. Whitney (1932), who established many fundamental results for it, later generalized the notion of a chromatic polynomial to that of an arbitrary graph. In 1968, Read asked whether it is possible to find a set of necessary and sufficient algebraic conditions for a polynomial to be the chromatic polynomial of some graph. In particular, Read asked for a necessary and sufficient condition for two graphs to be chromatically equivalent; that is, to have the same chromatic polynomial. In 1978, Chao and Whitehead defined a graph to be chromatically unique if no other graphs share its chromatic polynomial. Since then many researchers have been studying chromatic uniqueness and chromatic equivalence of graphs.

Item Type: | Monograph (Project Report) |
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Subjects: | Q Science > QA Mathematics |

Divisions: | Pusat Pengajian Sains Matematik (School of Mathematical Sciences) |

Depositing User: | Mr Erwan Roslan |

Date Deposited: | 25 Jan 2017 10:02 |

Last Modified: | 07 Sep 2017 12:47 |

URI: | http://eprints.usm.my/id/eprint/31793 |

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