Here are further materials on quandle coloring.

https://arxiv.org/pdf/1505.06595.pdf
In the paper, we explain the quandle coloring invariant and show how it can be handled computationally.

http://www.nusl.cz/ntk/nusl-387285
Master thesis of Martina Vavackova, where she proves the theorem that a T-coloring is invariant if and only if T is a graph of a quandle. She also explains other types of coloring invariants.

Quandles are the main topic of my research, if you are interested, I will happily tell you more!