Hmm. Not my favourite solution, but I think that the isomorphism checks can be done in batches, resulting in actual isomorph spaces, like this (for C5H10):

In any case, lets look at the simpler problem : listing non-isomorphic trees with max degree 3. It's a nice small example of a general approach that I've been thinking about. The idea is to:

Given N vertices, partition 2(N - 1) into N parts of at most 3 -> D = {d0, d1, ... }For each d_i in D, connect the degrees in all possible ways that make trees.Filter out duplicates within each set generated by some d_i. Hmm. Sure would be nice to have maths formatting on blogger....

Anyway, look at this example for partitioning 12 into 7 parts:

At the top are the partitions, in the middle the trees (colored by degree) …

## Comments

So, is this the result of a generation for C5H10 or has it already been filtered?

So, what I did was all-v-all check the structures produced from a single fragment combination (a single partition) as I assumed that there would only be duplicates within the children of a partition, and not between partition descendants.

Hmmm. I'll make a diagram..

Maybe there are recognizable patterns?

Eg:

10 = [[4, 4, 1, 1], [4, 3, 2, 1], [4, 2, 2, 2], [3, 3, 3, 1], [3, 3, 2, 2]]

In fact, it is also [[7, 1, 1, 1], [6, 2, 1, 1], [5, 3, 1, 1], [5, 2, 2, 1]] but those are rightly rejected for having valences greater than 4.