How exactly do these graphs work? Is each vertex supposed to represent an individual latin square? How are the edges related? I wish to understand more how these graphs are created. Thanks.

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Hello! Yes, each vertex is a unique diagonal Latin square. For every pair of vertices, they are connected by an edge if they are mutually orthogonal, and not connected otherwise. So, each graph is a complete mathematical structure, nothing to add and nothing to remove.

It is faster to reconstruct such a graph by just one pair of vertices + edge than to find all possible orthogonal pairs. That's why the search for pairs is done on BOINC, and the reconstruction of a full graph is done at the server.

I have found this result: https://rake.boincfast.ru/rakesearch/files/odls/R9_013835105_result.txt and am curious how it would graph. Is a result with 7 pairs in 3 squares more interesting than 7 pairs in 7 squares?

I have found this result: https://rake.boincfast.ru/rakesearch/files/odls/R9_013835105_result.txt and am curious how it would graph. Is a result with 7 pairs in 3 squares more interesting than 7 pairs in 7 squares?

Good result!

The first pair unfold to triple like R9_000716823/01.
The second set is part of a known large graph like R9_000037988/01 or other from top-3.
And the third pair raise to graph with 128 vertices and 1240 edges like R9_000154235/01.

Any result is very interesting because it may be a key to one of the structures, and maybe unknown structure!

Thank you and good luck!