Universal Journal of Mathematics and Mathematical Sciences
Volume 6, Issue 1, Pages 1 - 12
(July 2014)
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ON WARPING DEGREE OF VIRTUAL KNOT DIAGRAMS
Noureen A. Khan
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Abstract: Warping degree of knot diagram was studied by Kawauchi and Shimizu . In this paper, we extend the notion and introduce a new approach to find warping degree of a virtual knot diagram. We show that the sum of warping degrees of D and its inverse diagram satisfy the inequality: where c is the number of classical crossings of D. Furthermore, the equality holds if and only if D is an alternating diagram. |
Keywords and phrases: virtual knot, warping degree, knot diagrams, crossing number. |
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