Flyby graphs. Part 3

Message boards : News : Flyby graphs. Part 3

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Message 822 - Posted: 24 Mar 2019, 12:09:25 UTC
Last modified: 24 Mar 2019, 20:43:09 UTC

Dear participants!

On the preliminary results page, we publish the third part of Flyby graphs!

[R9_000715196_01] - 126 vertices and 512 edges. First graph with 126 vertices!

[R9_000715196_02] - 68 vertices and 392 edges. Third graph with 68 verices, but with high number of edges (146 and 185 in previous cases).

[R9_000716823_01] - 3 vertices and 3 edges. The main graph for this group! A tiny graph like triangle and not first case of triple mutually orthogonal diagonal Latin squares of order 9 (in some graphs published above we can see other groups), but a first graph (for rank 9), that consist from only 3 mutual orthogonal diagonal Latin squares! It is interesting that triples of ODLS are exists, although not often for rank 9 (as Fig. 176 or being parts of larger graphs). But for rank 10, they have not been found so far. Neither are they proven not to exist.

[R9_000833006_01] - 120 vertices and 360 edges. Third graph with 120 vertices, but graphs in previous cases contain 480 and 924 edges. Beautiful triangle-like graph!

[R9_000833006_02] - 40 vertices and 116 edges.

[R9_000916597_02] - 48 vertices and 105 edges. Sixth(!) graph with 48 vertices and with lowest number of edges.

[R9_000920565_09] - 24 vertices and 36 edges. Fifth graph with 24 vertices but with lowest number of edges also!

Thank you for your participation and happy crunching! :)
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Message boards : News : Flyby graphs. Part 3

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