Doctoral Degrees (Mathematical Sciences)
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Browsing Doctoral Degrees (Mathematical Sciences) by browse.metadata.advisor "Dorfling, Samantha"
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- ItemOn contributions to the theory of near-vector spaces and graphs thereof(Stellenbosch : Stellenbosch University, 2020-12) Wessels, Lesley Karin; Howell, Karin-Therese; Dorfling, Samantha; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Mathematics.ENGLISH ABSTRACT: In this thesis, our aim is to add to the existing body of work on near-vector spaces and their representation using graphs. We introduce two new graphs for constructions of nearvector spaces using finite fields, the fibration and subspace inclusion graph and study their properties. As a second focus, we look at the quotient spaces of a near-vector space, where some of the maximal regular subspaces have been factored out. For construction of nearvector spaces from copies of finite fields, we completely characterise regularity, describe the quasi-kernel and some of its graphs. We conclude with some reconstruction problems for the near-vector space graphs introduced and one related to finite near-fields.