doi: 10.7763/IJAPM.2013.V3.222
Equivalence of Dual Graphs
M. Azram
- the Department of Science, Faculty of Engineering, IIUM, Kuala Lumpur 50728, Malaysia
Abstract
Because of interesting and useful geometric as well as topological properties, alternating knots (links) were regarded to have an important role in knot theory and 3-manifold theory. Many knots with crossing number less than 10 are alternating. It was the properties of alternating knots that enable the earlier knot tabulators to construct tables with relatively few mistakes or omissions. Graphs of knots (links) have been repeatedly employed in knot theory. This article is devoted to establish relationship between knots and planar graphs. This relationship not only enables us see the equivalence of the graphs corresponding to black regions and the dual graph corresponding to white regions.
Keywords
- Dual graphs
- LR graphs
- planar isotopy
- R*-move
- reidmeister moves
How to Cite
M. Azram, "Equivalence of Dual Graphs," International Journal of Applied Physics and Mathematics, vol. 3, no. 4, pp. 286-288, 2013. https://doi.org/ 10.7763/IJAPM.2013.V3.222
Copyright & License
Copyright © 2013 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).