ON WARPING DEGREE OF VIRTUAL KNOT DIAGRAMS
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.
virtual knot, warping degree, knot diagrams, crossing number.