So recently I was asked about Király's method for generating all graphs from a degree sequence. While refactoring some of the code that I wrote to do this, I also made some tests. Specifically, coverage tests to check that the generation was actually exhaustive. I know it's redundant, but I have good tools to remove duplicate graphs - or I thought that I did…

Here a rough flowchart of the procedure here, starting with a number ('n') that is passed to Dreadnaut (the interface to nAUTy) to generate graphs:

These graphs are grouped by degree sequence, and these degree sequences are fed into the KirályHHGenerator to reconstruct the set of graphs. I think that compare arrow is wrong, but never mind. The point is that the sets should be the same size.

They are for n=5,6,7 but not for 8. Oddly enough, however, there are

However, two of my methods give different answers for this pair. The signatures method says they are different, while the partition refinement method says they are the same. Odd - and more investigation is needed before I am certain that

Here a rough flowchart of the procedure here, starting with a number ('n') that is passed to Dreadnaut (the interface to nAUTy) to generate graphs:

These graphs are grouped by degree sequence, and these degree sequences are fed into the KirályHHGenerator to reconstruct the set of graphs. I think that compare arrow is wrong, but never mind. The point is that the sets should be the same size.

They are for n=5,6,7 but not for 8. Oddly enough, however, there are

*more*in the Király set than in the nAUTy set. The obvious conclusion would be that my duplicate detection is failing - in other words, I am failing to spot an isomorphism between two graphs. For example this pair:However, two of my methods give different answers for this pair. The signatures method says they are different, while the partition refinement method says they are the same. Odd - and more investigation is needed before I am certain that

*geng*has missed some graphs here...
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