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 to investigate the relationship among the regions and crossings of a reduced alternating achiral knot but also their relationship to the vertices, edges and faces of the corresponding planar graphs. Consequently we have established an algorithm to construct reduced alternating achiral knots (links) through the planar graphs.
Page(s):
13-15
DOI:
DOI not available
Published:
Journal: Science International, Volume: 26, Issue: 1, Year: 2014