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dc.contributor.authorMacKeigan, Kyle
dc.date.accessioned2017-09-05T12:01:25Z
dc.date.available2017-09-05T12:01:25Z
dc.identifier.urihttp://hdl.handle.net/10222/73291
dc.description.abstractA total colouring of a graph is an assignment of colours to the edges and vertices such that adjacent objects receive different colours. In this thesis, we prove partial results towards the Total Colouring Conjecture which states that the total chromatic number of a graph is at most degree plus two. In the first part of this thesis there is an almost complete categorization of which total graphs are perfect. Upper bounds on the total chromatic number are found for Cartesian, strong, and tensor graph products. We determine that the total chromatic number of the Cartesian graph product depends strongly on the total chromatic number of the component graphs. Lastly, we explore how vertex multiplication affects the total chromatic number. We establish that for the star graph and cycle graph, no matter how many times a vertex is multiplied, the resulting graph satisfies the Total Colouring Conjecture.en_US
dc.language.isoenen_US
dc.subjectMathematicsen_US
dc.subjectTotal Colouringen_US
dc.subjectGraph Theoryen_US
dc.subjectGraph Productsen_US
dc.titleA Brief Exploration of Total Colouringen_US
dc.date.defence2017-08-28
dc.contributor.departmentDepartment of Mathematics & Statistics - Math Divisionen_US
dc.contributor.degreeMaster of Scienceen_US
dc.contributor.external-examinern/aen_US
dc.contributor.graduate-coordinatorDavid Ironen_US
dc.contributor.thesis-readerJason Brownen_US
dc.contributor.thesis-readerRichard Nowakowskien_US
dc.contributor.thesis-supervisorJeannette Janssenen_US
dc.contributor.ethics-approvalNot Applicableen_US
dc.contributor.manuscriptsNot Applicableen_US
dc.contributor.copyright-releaseNot Applicableen_US
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