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On the Degree Polynomial of Graphs

dc.contributor.authorGeorge, Ian
dc.contributor.copyright-releaseNot Applicableen_US
dc.contributor.degreeMaster of Scienceen_US
dc.contributor.departmentDepartment of Mathematics & Statistics - Math Divisionen_US
dc.contributor.ethics-approvalNot Applicableen_US
dc.contributor.external-examinern/aen_US
dc.contributor.graduate-coordinatorDavid Ironen_US
dc.contributor.manuscriptsNoen_US
dc.contributor.thesis-readerJeannette Janssenen_US
dc.contributor.thesis-readerRichard Nowakowskien_US
dc.contributor.thesis-supervisorJason Brownen_US
dc.date.accessioned2023-07-31T13:33:29Z
dc.date.available2023-07-31T13:33:29Z
dc.date.defence2023-07-25
dc.date.issued2023-07-28
dc.description.abstractGraph polynomials encode graph theoretic information in the form of polynomials. These polynomials have been of interest for decades, for both graph theoretic insight and their mathematical properties. This thesis discusses one particular graph polynomial: the degree polynomial. This graph polynomial encodes the degree sequence of a graph, and has only recently appeared in the literature. We begin by examining basic properties of the degree polynomial, including special evaluations. Our focus is largely on roots of the degree polynomial: we explore how these roots compare to roots of polynomials with non-negative integer coefficients, their density, and how they are impacted by restricting certain graph parameters. The latter leads to bounds on the roots in terms of graph order. We also study these roots for a few families of graphs, being able to say much more about their roots. Possible extensions or generalizations of the degree polynomial are also briefly discussed.en_US
dc.identifier.urihttp://hdl.handle.net/10222/82742
dc.language.isoenen_US
dc.subjectGraph polynomialen_US
dc.subjectDegreeen_US
dc.subjectPolynomial rootsen_US
dc.titleOn the Degree Polynomial of Graphsen_US

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