Abstract:
In this paper, we formulate a new local move on virtual knot
diagram, called arc shift move. Further, we extend it to another local
move called region arc shift defined on a region of a virtual knot diagram.
We establish that these arc shift and region arc shift moves are unknotting
operations by showing that any virtual knot diagram can be turned into
trivial knot using arc shift (region arc shift) moves. Based upon the arc
shift move and region arc shift move, we define two virtual knot invariants,
arc shift number and region arc shift number respectively.
