We give lower bounds for the Gordian distance and the unknotting number of handlebody-knots by using Alexander biquandle colorings. We construct handlebody-knots with Gordian distance $n$ and unknotting number $n$ for any positive integer $n$.
"The Gordian distance of handlebody-knots and Alexander biquandle colorings." J. Math. Soc. Japan 70 (4) 1247 - 1267, October, 2018. https://doi.org/10.2969/jmsj/77417741