# Finding the generators for automorphisms of a graph

Having a large graph, it will cause memory and kernel issues for SAGE to list all graph automorphisms. Is there a way to find the generators of the automorphisms instead of the whole automorphisms of a graph?

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Please provide an example of a graph where one encounters this problem.

( 2018-07-16 01:57:56 -0500 )edit

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As in your previous question, you can use the tab-completion and discover the gens method:

sage: G = graphs.PetersenGraph()
sage: A = G.automorphism_group()
sage: A.gens()
[(3,7)(4,5)(8,9),
(2,6)(3,8)(4,5)(7,9),
(1,4,5)(2,3,8,6,9,7),
(0,1)(2,4,6,5)(3,9,8,7)]


and even the gens_small one, which provides a small set of generators:

sage: A.gens_small()
[(0,5,7,2,1)(3,6,4,8,9), (0,9,8,2)(1,4,6,3)(5,7)]

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Thanks, it works. Just out of curiosity, what is the small set of generators?

( 2018-07-16 21:12:54 -0500 )edit

You can have a look at the documentation by doing:

sage: A.gens_small?


So, it provides a set of generators with small cardinality, however it is not necessarilly minimal.

( 2018-07-17 04:28:27 -0500 )edit