On folded cluster patterns of affine type

A cluster algebra is a commutative whose structure decided by skew-symmetrizable matrix or quiver. When invariant under an action of finite group and this admissible, the folded obtained from original one. Any non-simply-laced affine type can be folding simply-laced with specific $G$-action. In paper, we study combinatorial properties quivers in type. We prove that for any quiver type, $G$-invariance $G$-admissibility are equivalent. This leads us to set $G$-invariant seeds forms pattern.