# Virtual unknotting numbers of certain virtual torus knots

## TL;DR

This paper investigates the virtual unknotting number of specific virtual torus knots derived from classical torus knots, establishing that their virtual unknotting number equals the classical unknotting number.

## Contribution

It proves that for certain virtual torus knots obtained by virtualizing all crossings on one overstrand, the virtual unknotting number matches the classical unknotting number.

## Key findings

- Virtual unknotting number equals classical for these knots
- Unknotting number is (p-1)(q-1)/2 for the studied virtual knots
- Provides a method to compute virtual unknotting numbers in specific cases

## Abstract

The virtual unknotting number of a virtual knot is the minimal number of crossing changes that makes the virtual knot to be the unknot, which is defined only for virtual knots virtually homotopic to the unknot. We focus on the virtual knot obtained from the standard (p,q)-torus knot diagram by replacing all crossings on one overstrand into virtual crossings and prove that its virtual unknotting number is equal to the unknotting number of the $(p,q)$-torus knot, i.e. it is (p-1)(q-1)/2.