Delta Move Invariance of the L -Polynomials for Virtual Knots

We investigate when two virtual knots can be related by Δ-moves. We show that the L-polynomials are finite type invariants of order one. As a consequence, they are invariant under Δ-moves for any oriented virtual knot. As an application, we study virtual knots that can be converted into the trivial knot or the virtual knot 2.1 by a sequence of Δ-moves.