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dc.contributor.authorCameron, Benjamin
dc.date.accessioned2019-04-02T15:36:34Z
dc.date.available2019-04-02T15:36:34Z
dc.identifier.urihttp://hdl.handle.net/10222/75412
dc.description.abstractThe independence polynomial of a graph is a polynomial whose coefficients give the number of independent sets of each size. Its roots are called independence roots. This thesis explores the analytic properties of independence polynomials and the interactions between these properties and the structure of the corresponding graphs. We begin by applying results that relate the independence roots to the coefficients of independence polynomials of very well-covered graphs. We will explore families of graphs whose independence roots all lie to the left of the imaginary axis (which appears to be most graphs at a first glance) and other families of graphs that have independence roots to the right of this line. We then prove exponential bounds on the maximum modulus of an independence root that a graph of order $n$ can attain. Finally, we find graphs that are independence equivalent, that is have equivalent independence polynomial, to a path or a cycle of certain orders.en_US
dc.language.isoenen_US
dc.subjectgraphen_US
dc.subjectrooten_US
dc.subjectpolynomialen_US
dc.subjectindependence polynomialen_US
dc.subjectlog-concaveen_US
dc.titleOn the roots of independence polynomialsen_US
dc.date.defence2019-03-27
dc.contributor.departmentDepartment of Mathematics & Statistics - Math Divisionen_US
dc.contributor.degreeDoctor of Philosophyen_US
dc.contributor.external-examinerAdam Van Tuylen_US
dc.contributor.graduate-coordinatorDavid Ironen_US
dc.contributor.thesis-readerJeannette Janssenen_US
dc.contributor.thesis-readerRichard Nowakowskien_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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