Firstly we express the chromatic polynomials of some graphs in tree form. We then
Study a special product that comes natural and is useful in the calculation of some
Chromatic polynomials. Next we use the tree form to study the chromatic polynomial
Of a graph obtained from a forest (tree) by "blowing up" or "replacing" the vertices
Of the forest (tree) by a graph. Then we give explicit expressions, in terms of induced
Subgraphs, for the first five coefficients of the chromatic polynomial of a connected
Graph. In the case of higher order graphs we develop some useful computational
Techniques to obtain some higher order coefficients. In the process we obtain some
Useful combinatorial identities, some of which are new. We discuss in detail the
Application of these combinatorial identities to some families of graphs. We also discuss
Pairs of graphs that are chromatically equivalent and graph that are chromatically
Unique with special emphasis on wheels.
In conclusion,
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/20903 |
| Date | January 2016 |
| Creators | Adam, A A |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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