Eccentricity-based fault tolerance in graphs

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dc.contributor.advisorAllie, Imran
dc.contributor.advisorDu Preez, Brandon
dc.contributor.authorWade, Michael
dc.date.accessioned2026-07-01T11:04:38Z
dc.date.available2026-07-01T11:04:38Z
dc.date.issued2026
dc.date.updated2026-07-01T11:03:31Z
dc.description.abstractThe eccentricity of a vertex in a graph is the maximum length of a shortest path from that vertex to any other vertex in the graph. The eccentricity index of a graph is the sum of the eccentricities of the vertices in the graph. A fault in a graph is a vertex or edge deletion. In this thesis, we study eccentricity-based measures and properties of fault tolerance in graphs. Specifically, we study the change in the eccentricity of a vertex and the eccentricity index of a graph after edge or vertex deletions. We begin by discussing literature on edge-deleted eccentricity and edge-deleted eccentricity stable graphs. We then introduce vertex-deleted eccentricity and the average vertex-deleted eccentricity index of a graph and prove novel results regarding these concepts. Finally, we conclude by assessing the fault tolerance of common graphs in computer network design based on the measures discussed previously
dc.identifier.apacitationWade, M. (2026). <i>Eccentricity-based fault tolerance in graphs</i>. (). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/43443en_ZA
dc.identifier.chicagocitationWade, Michael. <i>"Eccentricity-based fault tolerance in graphs."</i> ., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2026. http://hdl.handle.net/11427/43443en_ZA
dc.identifier.citationWade, M. 2026. Eccentricity-based fault tolerance in graphs. . University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. http://hdl.handle.net/11427/43443en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Wade, Michael AB - The eccentricity of a vertex in a graph is the maximum length of a shortest path from that vertex to any other vertex in the graph. The eccentricity index of a graph is the sum of the eccentricities of the vertices in the graph. A fault in a graph is a vertex or edge deletion. In this thesis, we study eccentricity-based measures and properties of fault tolerance in graphs. Specifically, we study the change in the eccentricity of a vertex and the eccentricity index of a graph after edge or vertex deletions. We begin by discussing literature on edge-deleted eccentricity and edge-deleted eccentricity stable graphs. We then introduce vertex-deleted eccentricity and the average vertex-deleted eccentricity index of a graph and prove novel results regarding these concepts. Finally, we conclude by assessing the fault tolerance of common graphs in computer network design based on the measures discussed previously DA - 2026 DB - OpenUCT DP - University of Cape Town KW - eccentricity KW - graph, vertex LK - https://open.uct.ac.za PB - University of Cape Town PY - 2026 T1 - Eccentricity-based fault tolerance in graphs TI - Eccentricity-based fault tolerance in graphs UR - http://hdl.handle.net/11427/43443 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/43443
dc.identifier.vancouvercitationWade M. Eccentricity-based fault tolerance in graphs. []. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2026 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/43443en_ZA
dc.language.isoen
dc.language.rfc3066eng
dc.publisher.departmentDepartment of Mathematics and Applied Mathematics
dc.publisher.facultyFaculty of Science
dc.publisher.institutionUniversity of Cape Town
dc.subjecteccentricity
dc.subjectgraph, vertex
dc.titleEccentricity-based fault tolerance in graphs
dc.typeThesis / Dissertation
dc.type.qualificationlevelMasters
dc.type.qualificationlevelMSc
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