Criticality of the lower domination parameters of graphs

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dc.contributor.advisorGrobler, D. J. P.
dc.contributor.authorCoetzer, Audrey
dc.contributor.otherUniversity of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics.
dc.date.accessioned2008-07-15T10:27:48Zen_ZA
dc.date.accessioned2010-06-01T08:53:42Z
dc.date.available2008-07-15T10:27:48Zen_ZA
dc.date.available2010-06-01T08:53:42Z
dc.date.issued2007-03
dc.descriptionThesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007.
dc.description.abstractIn 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.en
dc.identifier.urihttp://hdl.handle.net/10019.1/2615
dc.language.isoen
dc.publisherStellenbosch : University of Stellenbosch
dc.rights.holderUniversity of Stellenbosch
dc.subjectIrredundanceen
dc.subjectIndependenceen
dc.subjectCriticalityen
dc.subjectDissertations -- Applied mathematicsen
dc.subjectTheses -- Applied mathematicsen
dc.subjectGraphic methodsen
dc.subjectDomination (Graph theory)en
dc.titleCriticality of the lower domination parameters of graphsen
dc.typeThesis
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