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dc.contributor.authorDeGagne, Corey
dc.date.accessioned2020-04-02T13:32:16Z
dc.date.available2020-04-02T13:32:16Z
dc.identifier.urihttp://hdl.handle.net/10222/78281
dc.description.abstractAssume that the vertices of a graph G are always operational, but the edges of G fail independently with probability q ∈ [0, 1]. The all-terminal reliability of G is the probability that the resulting subgraph is connected. The all-terminal reliability is a polynomial in q, and it was conjectured that all the roots of (nonzero) reliability polynomials fall inside the closed unit disk centred at 0. It has since been shown that there exist some connected graphs which have their reliability roots outside the closed unit disk, but these examples seem to be few and far between, and the roots are only barely outside the disk. In this dissertation we generalize the notion of reliability to simplicial complexes and matroids and investigate when the roots fall inside the closed unit disk. We then shift our attention to discuss a related problem – among all reliability polynomials of graphs on n vertices, which has a root of smallest modulus (that is, the distance from the root to the origin in the complex plane). We also show a mathematical statement that distinguishes the class of simple graphs from the class of all graphs using all- terminal reliability. Finally, we explore two-terminal reliability — in particular, the similarities and differences between two-terminal reliability polynomials and the all-terminal reliability, with a focus on their roots.en_US
dc.language.isoenen_US
dc.subjectnetwork reliabilityen_US
dc.subjectsimplicial complexen_US
dc.subjectmatroiden_US
dc.subjectpolynomial rootsen_US
dc.subjectall-terminalen_US
dc.subjecttwo-terminalen_US
dc.titleNetwork Reliability, Simplicial Complexes, and Polynomial Rootsen_US
dc.date.defence2020-03-16
dc.contributor.departmentDepartment of Mathematics & Statistics - Math Divisionen_US
dc.contributor.degreeDoctor of Philosophyen_US
dc.contributor.external-examinerBrett Stevensen_US
dc.contributor.graduate-coordinatorDavid Ironen_US
dc.contributor.thesis-readerSara Faridien_US
dc.contributor.thesis-readerDanielle Coxen_US
dc.contributor.thesis-supervisorJason Brownen_US
dc.contributor.ethics-approvalNot Applicableen_US
dc.contributor.manuscriptsNot Applicableen_US
dc.contributor.copyright-releaseNot Applicableen_US
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