A research report submitted to the Faculty of Science, in partial fulfilment of the requirements for the degree of Master of Science, University of the Witwatersrand. November 2014. / Knot theory is a branch of algebraic topology that is concerned with studying the
interesting geometrical structures known as knots. The idea of a knot in the theory
of knots is entirely different from everyday’s idea of knots, that is, a knot has free
ends. In knot theory a knot is defined as a knotted loop of string which does not have
free ends unless we cut it using a pair of scissors.
The interesting aspect of knot theory is that it enables us to transfer techniques
from graph theory, algebra, topology, group theory and combinatorics to study different
classes of knots. In this dissertation we are only concerned with the relationship
between knot theory and graph theory.
It is widely known in knot theory literature that a knot has a corresponding signed
planar graph and that a signed planar graph also has a corresponding knot which depends
on the signs of the edges of its signed planar graph. This provides a foundation
of a solid relationship between knot theory and graph theory, and it allows for some
of the notions in graph theory to be transferred to knot theory. In this dissertation
we study the path width and component number of links through their corresponding
graphs.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/17654 |
| Date | 07 May 2015 |
| Creators | Mdakane, Sizwe |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf, application/pdf, application/pdf |
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