Chromaticity of Certain 2-Connected Graphs
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 families of chromatically unique graphs and chromatically equivalent graphs. In Chapter 1, we...
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my-upm-ir.95952023-11-28T01:44:13Z Chromaticity of Certain 2-Connected Graphs 2003-01 Lau, Gee Choon 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 families of chromatically unique graphs and chromatically equivalent graphs. In Chapter 1, we define the concept of graph colouring, the associated chromatic polynomial and some properties of a chromatic polynomial. We also give some necessary conditions for graphs that are chromatically unique or chromatically equivalent. Chapter 2 deals with the chromatic classes of certain existing 2-connected (n, n + 1,)-graphs for z = 0, 1, 2 and 3. Many families of chromatically unique graphs and chromatically equivalent graphs of these classes have been obtained. At the end of the chapter, we re-determine the chromaticity of two families of 2-connected (n, n + 3)-graphs with at least two triangles. Our main results in this thesis are presented in Chapters 3, 4 and 5. In Chapter 3, we classify all the 2-connected (n, n + 4)-graphs wit h at least four triangles . In Chapter 4 , we classify all the 2-connected (n, n + 4)-graphs wit h t hree triangles and one induced 4-cycle. In Chapter 5, we classify all the 2-connected (n, n + 4)graphs with three triangles and at least two induced 4-cycles . In each chapter, we obtain new families of chromatically unique graphs and chromatically equivalent graphs. We end the thesis by classifying all the 2-connected (n, n + 4)-graphs with exactly three triangles. We also determine the chromatic polynomial of all these graphs. The determination of the chromaticity of most classes of these graphs is left as an open problem for future research. Algebras, Linear 2003-01 Thesis http://psasir.upm.edu.my/id/eprint/9595/ http://psasir.upm.edu.my/id/eprint/9595/1/FSAS_2003_48_IR.pdf text en public masters Universiti Putra Malaysia Algebras, Linear Faculty of Science and Environmental Studies Peng, Yee Hock English |
| institution |
Universiti Putra Malaysia |
| collection |
PSAS Institutional Repository |
| language |
English English |
| advisor |
Peng, Yee Hock |
| topic |
Algebras Linear |
| spellingShingle |
Algebras Linear Lau, Gee Choon Chromaticity of Certain 2-Connected Graphs |
| 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 families of chromatically unique
graphs and chromatically equivalent graphs.
In Chapter 1, we define the concept of graph colouring, the associated chromatic
polynomial and some properties of a chromatic polynomial. We also give some
necessary conditions for graphs that are chromatically unique or chromatically
equivalent.
Chapter 2 deals with the chromatic classes of certain existing 2-connected (n, n + 1,)-graphs for z = 0, 1, 2 and 3. Many families of chromatically unique graphs and
chromatically equivalent graphs of these classes have been obtained. At the end
of the chapter, we re-determine the chromaticity of two families of 2-connected
(n, n + 3)-graphs with at least two triangles. Our main results in this thesis are presented in Chapters 3, 4 and 5. In Chapter
3, we classify all the 2-connected (n, n + 4)-graphs wit h at least four triangles . In
Chapter 4 , we classify all the 2-connected (n, n + 4)-graphs wit h t hree triangles
and one induced 4-cycle. In Chapter 5, we classify all the 2-connected (n, n + 4)graphs
with three triangles and at least two induced 4-cycles . In each chapter, we
obtain new families of chromatically unique graphs and chromatically equivalent
graphs.
We end the thesis by classifying all the 2-connected (n, n + 4)-graphs with exactly
three triangles. We also determine the chromatic polynomial of all these graphs.
The determination of the chromaticity of most classes of these graphs is left as
an open problem for future research. |
| format |
Thesis |
| qualification_level |
Master's degree |
| author |
Lau, Gee Choon |
| author_facet |
Lau, Gee Choon |
| author_sort |
Lau, Gee Choon |
| title |
Chromaticity of Certain 2-Connected Graphs |
| title_short |
Chromaticity of Certain 2-Connected Graphs |
| title_full |
Chromaticity of Certain 2-Connected Graphs |
| title_fullStr |
Chromaticity of Certain 2-Connected Graphs |
| title_full_unstemmed |
Chromaticity of Certain 2-Connected Graphs |
| title_sort |
chromaticity of certain 2-connected graphs |
| granting_institution |
Universiti Putra Malaysia |
| granting_department |
Faculty of Science and Environmental Studies |
| publishDate |
2003 |
| url |
http://psasir.upm.edu.my/id/eprint/9595/1/FSAS_2003_48_IR.pdf |
| _version_ |
1794018852827299840 |