Hasni, Roslan (2009) An attempt to classify bipartite graphs by their chromatic Polynomial. Project Report. Universiti Sains Malaysia. (Submitted)
Full text not available from this repository.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) |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Pusat Pengajian Sains Matematik (School of Mathematical Sciences) |
| Depositing User: | Mr Erwan Roslan |
| Date Deposited: | 25 Jan 2017 02:02 |
| Last Modified: | 07 Sep 2017 04:47 |
| URI: | http://eprints.usm.my/id/eprint/31793 |
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