[Nauty] Generating all possible automorfisms from given graph

[Sterten at aol.com]

 >Hello!
 >Can you give me an example of an infile? How it must
 >look?

take for example the 11 graphs with n=4 ,
put into a file "graph4" looking like this :

0000 0000 0000 0000
0000 0000 0001 0010
0000 0001 0001 0110
0000 0011 0101 0110
0001 0001 0001 1110
0001 0010 0100 1000
0001 0010 0101 1010
0001 0011 0101 1110
0011 0011 1100 1100
0011 0011 1101 1110
0111 1011 1101 1110

11 rows with 16 1s or 0s each. Blanks or commas are ignored.
You should be able to do the same for Nauty-formats or 
Dimacs format or others. 
However I use this one, because it's human readable.

now I type 
gauto graph4
to get the sizes of the automorphism groups :

24
4
2
6
6
8
2
2
8
4
24

or I type 
gauto graph4 42
to get lists of generators for the 11 automorphism groups :

(2 3)
(1 2)
(0 1)
4 24
(2 3)
(0 1)
4 4
(1 2)
4 2
(2 3)
(1 2)
4 6
(1 2)
(0 1)
4 6
(1 2)
(0 1)(2 3)
4 8
(0 1)(2 3)
4 2
(1 2)
4 2
(2 3)
(0 1)
(0 2)(1 3)
4 8
(2 3)
(0 1)
4 4
(2 3)
(1 2)
(0 1)
4 24

grr... I don't like this output, I should change the program
to get the output like this :

4,24 : (2,3),(1,2),(0,1)
4, 4 : (2,3),(0,1)
4, 2 : (1,2)
4, 6 : (2,3),(1,2)
4, 6 : (1,2),(0,1)
4, 8 : (1,2),(0,1)(2,3)
4, 2 : (0,1)(2,3)
4, 2 : (1,2)
4, 8 : (2,3),(0,1),(0,2)(1,3)
4, 4 : (2,3),(0,1)
4,24 : (2,3),(1,2),(0,1)

note, that the side right from the ":" has permutations of (0,1,2,3)
in cycle - notation separated by commas. 
They generate a subgroup of S({0,1,2,3}) of the size specified on the
left side.
It's not very practicable to give all automorphisms explicitely,
since there can be whole lot of them.
But you can generate them all, if necessary from the generators.

BTW., are the generators always chosen "canonical" , so that 
the groups are isomorphic, iff the lists of generators coincide ?


Guenter

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