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.

Index Terms—Dual graphs, LR graphs, planar isotopy, R*-move, reidmeister moves.

M. Azram is with the Department of Science, Faculty of Engineering, IIUM, Kuala Lumpur 50728, Malaysia (e-mail: azram50@hotmail.com).

Cite:M. Azram, "Equivalence of Dual Graphs," International Journal of Applied Physics and Mathematics vol. 3, no. 4, pp. 286-288, 2013.