Knots Verses Graphs
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....
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2011
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| Online Access: | http://irep.iium.edu.my/2655/ http://irep.iium.edu.my/2655/ http://irep.iium.edu.my/2655/1/ICTA%28K%29.pdf |
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iium-26552011-12-29T04:38:16Z http://irep.iium.edu.my/2655/ Knots Verses Graphs Azram, Mohammad QA Mathematics 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. 2011 Conference or Workshop Item NonPeerReviewed application/pdf en http://irep.iium.edu.my/2655/1/ICTA%28K%29.pdf Azram, Mohammad (2011) Knots Verses Graphs. In: International Conference on Topology and its Applications, 4-10 July 2011, Islamabad. (Unpublished) http://atlas-conferences.com/cgi-bin/abstract/cbbk-53 |
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Digital Repository |
| institution_category |
Local University |
| institution |
International Islamic University Malaysia |
| building |
IIUM Repository |
| collection |
Online Access |
| language |
English |
| topic |
QA Mathematics |
| spellingShingle |
QA Mathematics Azram, Mohammad Knots Verses Graphs |
| description |
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.
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| format |
Conference or Workshop Item |
| author |
Azram, Mohammad |
| author_facet |
Azram, Mohammad |
| author_sort |
Azram, Mohammad |
| title |
Knots Verses Graphs
|
| title_short |
Knots Verses Graphs
|
| title_full |
Knots Verses Graphs
|
| title_fullStr |
Knots Verses Graphs
|
| title_full_unstemmed |
Knots Verses Graphs
|
| title_sort |
knots verses graphs |
| publishDate |
2011 |
| url |
http://irep.iium.edu.my/2655/ http://irep.iium.edu.my/2655/ http://irep.iium.edu.my/2655/1/ICTA%28K%29.pdf |
| first_indexed |
2023-09-18T20:10:16Z |
| last_indexed |
2023-09-18T20:10:16Z |
| _version_ |
1777407431000719360 |