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Criticality of the lower domination parameters of graphs
Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : University of Stellenbosch
2008
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| _version_ | 1867614054596476928 |
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| access_status_str | Open Access |
| author | Coetzer, Audrey |
| author2 | Grobler, D. J. P. |
| author_browse | Coetzer, Audrey Grobler, D. J. P. |
| author_facet | Grobler, D. J. P. Coetzer, Audrey |
| author_sort | Coetzer, Audrey |
| collection | Thesis |
| dc_rights_str_mv | University of Stellenbosch |
| description | Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/2615 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:45:56.159Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2008 |
| publishDateRange | 2008 |
| publishDateSort | 2008 |
| publisher | Stellenbosch : University of Stellenbosch |
| publisherStr | Stellenbosch : University of Stellenbosch |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/2615 Criticality of the lower domination parameters of graphs Coetzer, Audrey Grobler, D. J. P. University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics. Irredundance Independence Criticality Dissertations -- Applied mathematics Theses -- Applied mathematics Graphic methods Domination (Graph theory) 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. 2008-07-15T10:27:48Z 2010-06-01T08:53:42Z 2008-07-15T10:27:48Z 2010-06-01T08:53:42Z 2007-03 Thesis http://hdl.handle.net/10019.1/2615 en University of Stellenbosch application/pdf Stellenbosch : University of Stellenbosch |
| spellingShingle | Irredundance Independence Criticality Dissertations -- Applied mathematics Theses -- Applied mathematics Graphic methods Domination (Graph theory) Coetzer, Audrey Criticality of the lower domination parameters of graphs |
| title | Criticality of the lower domination parameters of graphs |
| title_full | Criticality of the lower domination parameters of graphs |
| title_fullStr | Criticality of the lower domination parameters of graphs |
| title_full_unstemmed | Criticality of the lower domination parameters of graphs |
| title_short | Criticality of the lower domination parameters of graphs |
| title_sort | criticality of the lower domination parameters of graphs |
| topic | Irredundance Independence Criticality Dissertations -- Applied mathematics Theses -- Applied mathematics Graphic methods Domination (Graph theory) |
| url | http://hdl.handle.net/10019.1/2615 |
| work_keys_str_mv | AT coetzeraudrey criticalityofthelowerdominationparametersofgraphs |