automorphism of a graph
 
  
 
  
 
 
 
 
 
 
    
        
        asked 0 years ago  
 
 salam gravatar image  
 
 
 
 
    
        
        updated 0 years ago  
 
 FrédéricC gravatar image  
 
 
 
 
 
I was wondering if someone could help me determine whether a graph admits a semiregular automorphism, based on the following definition.
 
A non-identity automorphism of a graph is semiregular, in particular, (k,n)-semiregular if it has k cycles of equal length n in its cycle decomposition. 
 
Thank you so much.
 
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Are k and n given?
Max Alekseyev gravatar imageMax Alekseyev (
    
        0 years ago
    )
For given k, for instance (3,n)-semiregular .
salam gravatar imagesalam (
    
        0 years ago
    )
@Max Alekseyev, I wrote the code, but it seems that it fails.
def is_m_n_semiregular_automorphism(G, m, n):
aut_group = G.automorphism_group()
for perm in aut_group:
    cycle_decomposition = perm.cycle_type() 
    if cycle_decomposition == (n,) * m:  
        return True
return False
salam gravatar imagesalam (
    
        0 years ago
    )
You are comparing a partition to a tuple. An easy fix:
cycle_decomposition = tuple( perm.cycle_type() )
Max Alekseyev gravatar imageMax Alekseyev (
    
        0 years ago
    )
Thanks a lot.
salam gravatar imagesalam (
    
        0 years ago
    )
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