Iterate through all trees of a given size

Question

I am often faced with the problem of checking some property of trees (the graph ones) of a given size by brute force. Do you have any nice tricks for doing this? Ideally, I'd like to examine each isomorphism class only once (but after all, speed is all that matters).

Bit twiddling tricks are most welcome since n is usually less than 32 :)

I'm asking for slightly more refined algorithms than the likes of "loop through all (n-1)-edge subsets and check if they form a tree" for trees on n nodes.

Answer 1

This is in Knuth's The Art of Computer Programming volume on Combinatorial Algorithms. If I remember correctly, it's an exercise there. Since he has the solutions for such, I point you there.