Satoh and Taniguchi introduced the Formula: see text-writhe Formula: see text for each non-zero integer Formula: see text, which is an integer invariant for virtual knots. It is obvious that the virtualization of a real crossing is an unknotting operation for virtual knots. In our previous paper, we showed that if Formula: see text is a sequence of integers with Formula: see text, then there exists a virtual knot Formula: see text whose virtual unknotting number equals one and Formula: see text for any Formula: see text. In this paper we show that there exist infinitely many virtual knots having such properties by using the vertex connected sum on Gauss diagrams.
OHYAMA et al. (Wed,) studied this question.