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):
Well, I had been hoping to reject isomorphs without doing an all-v-all check with the UIT. Sadly this didn't work - at least with the tests that I thought of.
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.
Um, well the partitions are just lists of numbers. There may be all sorts of interesting patterns in them, but mostly of interest to number theorists, not chemists :)
After cubane, the thought occurred to look at other regular hydrocarbons. If only there was some sort of classification of chemicals that I could use look up similar structures. Oh wate, there is . Anyway, adamantane is not as regular as cubane, but it is highly symmetrical, looking like three cyclohexanes fused together. The vertices fall into two different types when colored by signature: The carbons with three carbon neighbours (degree-3, in the simple graph) have signature (a) and the degree-2 carbons have signature (b). Atoms of one type are only connected to atoms of another - the graph is bipartite . Adamantane connects together to form diamondoids (or, rather, this class have adamantane as a repeating subunit). One such is diamantane , which is no longer bipartite when colored by signature: It has three classes of vertex in the simple graph (a and b), as the set with degree-3 has been split in two. The tree for signature (c) is not shown. The graph is still bipartite accordin...
I wanted to show something that hints at the things that the new architecture can afford us: This is using a Java2D graphics Paint object to make it look like chalk...kindof. It's a very simplistic way of doing it by making a small image with a random number of white, gray, lightgray, and black pixels. edit: it doesn't look so good at small scales some tweaking of stroke widths and so on is essential.
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.