In case it's useful, I mindlessly copied all the data about trees from the thesis and [rendered them here](https://tinyurl.com/3zjuhyvu). I've noted the parent vector actually used for rendering but output some other arrays like a depth vector before processing or a raw parent vector before resorting into DFS preorder.
A few look funny which may well be my bugs. I'll have a closer look at some point.
In any event, take it for what it's worth.