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Knots Verses Graphs

Azram, Mohammad (2011) Knots Verses Graphs. In: International Conference on Topology and its Applications, 4-10 July 2011, Islamabad. (Unpublished)

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Abstract

A theoretic and diagrammatic relationship between knots and planar graphs has enabled us to visualize, redefine and establish some variational, diagrammatic and illustrative results. It has been shown that the universes, LR-graphs and regions of reduced alternating knots (links) are path connected. Connected universe corresponding to reduced alternating knot (link) is unique. It has been shown that the regions, crossings and consequently the number of vertices, edges, and faces in the corresponding LR-graph are same and invariant. Establishment of new but pivotal moves such as R*-move, 2π-twist and π-twist enabled us to change connected knot (link) into a reduced form as well as to prove that the black regions can be changed into white regions via Reidemeister moves. It has been established that for reduced alternating knot (linked link), total regions are two more than the total crossings. In case the knot (linked link) is also achiral than total crossings = 2[total black(white) regions-1]. Finally, the equivalence of the companion graphs, necessary and sufficient conditions for achirality.

Item Type: Conference or Workshop Item (Keynote)
Additional Information: 3127/2655
Uncontrolled Keywords: Achiral knots
Subjects: Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes: Kulliyyah of Engineering > Department of Science
Depositing User: Prof Mohammad Azram
Date Deposited: 13 Sep 2011 09:43
Last Modified: 29 Dec 2011 12:38
URI: http://irep.iium.edu.my/id/eprint/2655

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