To record what has happened, ancient people tie knots. I. C/zing, the Chinese classic of 1027-771 BC. Knots are fascinating objects. When fastening a rope, the distinction between a knot and a 'slip-knot' (one that can be undone by pulling) must have been recognized very early in human history. We
Dual graphs and knot invariants
β Scribed by Magnhild Lien; William Watkins
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 159 KB
- Volume
- 306
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We consider the equivalence classes of graphs induced by the unsigned versions of the Reidemeister moves on knot diagrams. Any graph that is reducible by some finite sequence of these moves, to a graph with no edges, is called a knot graph. We show that the class of knot graphs strictly contains the
A (tame) link can be defined as a finite collection of disjoint polygons embedded in Euclidean 3-space. Links are usually represented by plane projections, or diagrams, which can be viewed as 4-regular plane graphs with signed vertices. Then the 3-dimensional concept of ambient isotopy of links can
This paper presents a knot theoretic approach to the study of molecular graphs. It provides examples of molecular knots and links as well as other topologically complex molecules. The paper discusses various topological problems and theorems which were motivated by questions in chemistry. Some of th