automorphism of a graph

asked 2024-12-30 17:38:52 +0100

salam gravatar image

updated 2024-12-31 08:44:49 +0100

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.

edit retag flag offensive close merge delete

Comments

Are $k$ and $n$ given?

Max Alekseyev gravatar imageMax Alekseyev ( 2024-12-31 01:35:40 +0100 )edit

For given k, for instance (3,n)-semiregular .

salam gravatar imagesalam ( 2024-12-31 13:36:58 +0100 )edit

@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 ( 2024-12-31 15:33:17 +0100 )edit

You are comparing a partition to a tuple. An easy fix:

cycle_decomposition = tuple( perm.cycle_type() )
Max Alekseyev gravatar imageMax Alekseyev ( 2024-12-31 16:54:24 +0100 )edit

Thanks a lot.

salam gravatar imagesalam ( 2024-12-31 17:04:39 +0100 )edit
add a comment