[Nauty] Isomorphism test of labeled graphs

[Jacek P Kukluk]

Hi
 
I am calling nauty functions to test isomorphism in larger program. I
tested successfully unlabeled graphs. I need help in understanding how
to use nauty for graphs with labels. For example the two graphs below
are not isomorphic because they have different labels. 
 
G1= 
A--------------------------A
  |                                  |
  |                                  |
 A--------------------------A
 
G2= 
A--------------------------A
  |                                  |
  |                                  |
 B--------------------------B
 
According to nauty user;s guide I can use graph *g to represent the
structure and arrays int  *lab, *ptn to represent labels as colors. My
representation of G1 is 
  0 :  1 3;
  1 :  0 2;
  2 :  1 3;
  3 :  0 2;
lab[0]=0;   lab[1]=1;   lab[2]=2;  lab[3]=3;
ptn[0]=1;   ptn[1]=1;   ptn[2]=1;  ptn[3]=0;
 
G2 
  0 :  1 3;
  1 :  0 2;
  2 :  1 3;
  3 :  0 2;
lab[0]=0;   lab[1]=1;   lab[2]=2;   lab[3]=3;
ptn[0]=1;   ptn[1]=0;   ptn[2]=2;   ptn[3]=0;
 
I am setting 
options.defaultptn = FALSE;
and using modified dreadnaut to check isomorphism. I am comparing if the
contents of canong produced by nauty for both graphs is the same. It
works well for unlabeled graphs but seems to be not enough for labeled
graphs.  What additional checking should I do? 
 
What would be the proper use of lab, ptn and nauty with labeled graphs,
as in this case? How should I represent G1 and G2 if all vertices of G1
would be labeled A and all vertices of G2 labeled B?
 
I will greatly appreciate any suggestion. 
 
Jacek
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