Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007. / In this thesis we focus on the lower domination parameters of a graph G, denoted ¼(G), for
¼ 2 {i, ir, °}. For each of these parameters, we are interested in characterizing the structure of
graphs that are critical when faced with small changes such as vertex-removal, edge-addition and
edge-removal. While criticality with respect to independence and domination have been well
documented in the literature, many open questions still remain with regards to irredundance.
In this thesis we answer some of these questions.
First we describe the relationship between transitivity and criticality. This knowledge we then
use to determine under which conditions certain classes of graphs are critical. Each of the
chosen classes of graphs will provide specific examples of different types of criticality. We also
formulate necessary conditions for graphs to be ir-critical and ir-edge-critical.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/2615 |
| Date | 03 1900 |
| Creators | Coetzer, Audrey |
| Contributors | Grobler, D. J. P., University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics. |
| Publisher | Stellenbosch : University of Stellenbosch |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Rights | University of Stellenbosch |
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