Abstract
For classical knots, clasp pass moves are closely related to Vassiliev invariants of degree [Formula: see text]. Tsukamoto showed that the values of the Vassiliev invariant of degree [Formula: see text] induced from the Jones polynomial for two knots differ by [Formula: see text] or [Formula: see text], if they are related by a single clasp pass move. For virtual knots, the arrow polynomial is a generalization of the Jones polynomial and induces a Vassiliev invariant of degree [Formula: see text]. We show that the values of the Vassiliev invariant of degree [Formula: see text] induced from the arrow polynomial of two virtual knots differ by [Formula: see text] or [Formula: see text], if they are related by a single clasp pass move. We also obtain a lower bound of the distance between virtual knots by clasp pass moves.
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