[Nauty-list] geng 33 vertices and diameter 2
Gunnar.Brinkmann at ugent.be
Wed Oct 19 18:26:01 EST 2005
Hoang Minh Nguyen wrote:
> At the moment geng is limited to generating graphs of order up to
>32. It seems that this restriction is due to the data structure used to
>store intermediate graphs?
>I would like to know if there is a way to modify geng to generate ALL graphs
>of order 33 with the restriction that the diameter of each graph is 2.
>Is there a good way to speed up the search given the diameter restriction?
>It might be a hard problem but just ask in case someone has any idea :-).
There is a special programn that generates diameter 2 graphs if you have
restriction that they are triangle free. But even with this additional
restriction there are
__FAR__ too many to generate them all.
Just think about the following: take an arbitrary graph with n vertices
and add a new
vertex neighbouring all of the previous n vertices. This is a diameter 2
(or 1) graph on n+1
vertices. I'm not talking about isomorphism here, but it gives you an
idea that restricting
the diameter to 2 doesn't help you get much further than when generating
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