An unknotting index for virtual links

Abstract

Given a virtual link diagram D, we define its unknotting index U(D)to be minimum among (m, n)tuples, where mstands for the number of crossings virtualized and nstands for the number of classical crossing changes, to obtain a trivial link diagram. By using span of a diagram and linking number of a diagram we provide a lower bound for unknotting index of a virtual link. Then using warping degree of a diagram, we obtain an upper bound. Both these bounds are applied to find unknotting index for virtual links obtained from pretzel links by virtualizing some crossings.