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Gordian complex of knots was defined by Hirasawa and Uchida as the simplicialcomplex whose vertices are knot isotopy classes in $\mathbb{S}^3$. LaterHoriuchi and Ohyama defined Gordian complex of virtual knots using $v$-move andforbidden moves. In this paper we discuss Gordian complex of knots by regioncrossing change and Gordian complex of virtual knots by arc shift move. Arcshift move is a local move in the virtual knot diagram which results inreversing orientation locally between two consecutive crossings. We show theexistence of an arbitrarily high dimensional simplex in both the Gordiancomplexes, i.e., by region crossing change and by the arc shift move. For anygiven knot (respectively, virtual knot) diagram we construct an infinite familyof knots (respectively, virtual knots) such that any two distinct members ofthe family have distance one by region crossing change (respectively, arc shiftmove). We show that that the constructed virtual knots have the same affineindex polynomial.

Gordian complexes of knots and virtual knots given by region crossing changes and arc shift moves