Citation
Lau, Gee Choon
(2003)
Chromaticity of Certain 2Connected Graphs.
Masters thesis, Universiti Putra Malaysia.
Abstract
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 2connected (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 redetermine the chromaticity of two families of 2connected
(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 2connected (n, n + 4)graphs wit h at least four triangles . In
Chapter 4 , we classify all the 2connected (n, n + 4)graphs wit h t hree triangles
and one induced 4cycle. In Chapter 5, we classify all the 2connected (n, n + 4)graphs
with three triangles and at least two induced 4cycles . In each chapter, we
obtain new families of chromatically unique graphs and chromatically equivalent
graphs.
We end the thesis by classifying all the 2connected (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.
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