Equivalence of dual graphs
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 ena...
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| Format: | Article |
| Language: | English |
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International Association of Computer Science and Information Technology Press (IACSIT)
2013
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| Online Access: | http://irep.iium.edu.my/30518/ http://irep.iium.edu.my/30518/ http://irep.iium.edu.my/30518/1/222-P2008.pdf |
| Summary: | 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. |
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