Invariants of handlebody-knots via yokota's invariants

We construct quantum $\mathcal{U}-q(\mathfrak{sl}-{2})$ type invariants for handlebody-knots in the 3-sphere S³. A handlebody-knot is an embedding of a handlebody in a 3-manifold. These invariants are linear sums of Yokota's invariants for colored spatial graphs which are defined by using the Kauffman bracket. We give a table of calculations of our invariants for genus 2 handlebody-knots up to six crossings. We also show our invariants are identified with special cases of the Witten-Reshetikhin-Turaev invariants.