Chromatic uniqueness of certain complete tripartite graphs with some edges deleted / Lau Gee Choon and Chu Hong Heng
Since the introduction of the concepts of chromatically unique graphs and chromatically equivalent graphs, many families of such graphs have been obtained. In this thesis, we continue with the search of new families of chromatically unique graphs In Chapter 1, we define the concept of graph colourin...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Research Reports |
| Language: | en |
| Published: |
Institute of Research, Development and Commercialization, Universiti Teknologi MARA
2005
|
| Subjects: | |
| Online Access: | https://ir.uitm.edu.my/id/eprint/7973/2/7973.PDF https://ir.uitm.edu.my/id/eprint/7973/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1833058447248064512 |
|---|---|
| author | Lau, Gee Choon Chu, Hong Heng |
| author_facet | Lau, Gee Choon Chu, Hong Heng |
| author_sort | Lau, Gee Choon |
| building | Tun Abdul Razak Library |
| collection | Institutional Repository |
| content_provider | Universiti Teknologi Mara |
| content_source | UiTM Institutional Repository |
| continent | Asia |
| country | Malaysia |
| description | Since the introduction of the concepts of chromatically unique graphs and chromatically equivalent graphs, many families of such graphs have been obtained. In this thesis, we continue with the search of new families of chromatically unique graphs In Chapter 1, we define the concept of graph colouring, the associated chromatic polynomial and some properties of chromatic polynomial. We also give some necessary conditions for graphs that are chromatically unique or chromatically equivalent. Chapter 2 begins with the definition of complete tripartite graphs and some preliminary results related to complete tripartite graphs. In particular, certain chromatically unique complete tripartite graphs are given. Some new chromatically unique complete tripartite graphs are then presented at the end of this chapter. In Chapter 3, we first give some necessary conditions for complete tripartite graphs with some edges deleted to be chromatically equivalent. We then proved that certain complete tripartite graphs with one edge deleted are also chromatically unique. The determination of the chromaticity of other complete tripartite graphs with certain edges deleted is left as an open problem for future research. We end the thesis by making a conjecture that all complete tripartite graphs with each partite set having at least two
vertices are chromatically unique. |
| format | Research Reports |
| id | my.uitm.ir-7973 |
| institution | Universiti Teknologi Mara |
| language | en |
| publishDate | 2005 |
| publisher | Institute of Research, Development and Commercialization, Universiti Teknologi MARA |
| record_format | eprints |
| spelling | my.uitm.ir-79732024-08-19T16:37:56Z https://ir.uitm.edu.my/id/eprint/7973/ Chromatic uniqueness of certain complete tripartite graphs with some edges deleted / Lau Gee Choon and Chu Hong Heng Lau, Gee Choon Chu, Hong Heng Algebra Since the introduction of the concepts of chromatically unique graphs and chromatically equivalent graphs, many families of such graphs have been obtained. In this thesis, we continue with the search of new families of chromatically unique graphs In Chapter 1, we define the concept of graph colouring, the associated chromatic polynomial and some properties of chromatic polynomial. We also give some necessary conditions for graphs that are chromatically unique or chromatically equivalent. Chapter 2 begins with the definition of complete tripartite graphs and some preliminary results related to complete tripartite graphs. In particular, certain chromatically unique complete tripartite graphs are given. Some new chromatically unique complete tripartite graphs are then presented at the end of this chapter. In Chapter 3, we first give some necessary conditions for complete tripartite graphs with some edges deleted to be chromatically equivalent. We then proved that certain complete tripartite graphs with one edge deleted are also chromatically unique. The determination of the chromaticity of other complete tripartite graphs with certain edges deleted is left as an open problem for future research. We end the thesis by making a conjecture that all complete tripartite graphs with each partite set having at least two vertices are chromatically unique. Institute of Research, Development and Commercialization, Universiti Teknologi MARA 2005 Research Reports NonPeerReviewed text en https://ir.uitm.edu.my/id/eprint/7973/2/7973.PDF Chromatic uniqueness of certain complete tripartite graphs with some edges deleted / Lau Gee Choon and Chu Hong Heng. (2005) [Research Reports] <http://terminalib.uitm.edu.my/7973.pdf> (Unpublished) |
| spellingShingle | Algebra Lau, Gee Choon Chu, Hong Heng Chromatic uniqueness of certain complete tripartite graphs with some edges deleted / Lau Gee Choon and Chu Hong Heng |
| title | Chromatic uniqueness of certain complete tripartite graphs with some edges deleted / Lau Gee Choon and Chu Hong Heng |
| title_full | Chromatic uniqueness of certain complete tripartite graphs with some edges deleted / Lau Gee Choon and Chu Hong Heng |
| title_fullStr | Chromatic uniqueness of certain complete tripartite graphs with some edges deleted / Lau Gee Choon and Chu Hong Heng |
| title_full_unstemmed | Chromatic uniqueness of certain complete tripartite graphs with some edges deleted / Lau Gee Choon and Chu Hong Heng |
| title_short | Chromatic uniqueness of certain complete tripartite graphs with some edges deleted / Lau Gee Choon and Chu Hong Heng |
| title_sort | chromatic uniqueness of certain complete tripartite graphs with some edges deleted / lau gee choon and chu hong heng |
| topic | Algebra |
| url | https://ir.uitm.edu.my/id/eprint/7973/2/7973.PDF https://ir.uitm.edu.my/id/eprint/7973/ |
| url_provider | http://ir.uitm.edu.my/ |