Dear sir,
there is an error concerning the function "is_prime" for graphs in
Sagemath, section Graph Theory.
Here is a conter-example.
g1=Graph({0:[1,4],1:[0,2,4],2: [1,3,4],3:[2],4:[0,1,2]});g2=G
raph({0:[1],1:[0,2,4],2:[1,3,4 ],3:[2,4],4:[1,2,3]})
#g1.show();g2.show();
#[1,4] is a module of g1 so g1 is not prime
#[2,4] is a module of g2 so g2 is not prime
g2.is_isomorphic(g1), g1.is_prime(),g2.is_prime()
This is a conter-example with two isomorphic graphs g1 and g2 on 5
vertices giving two different results
with the function "is prime".
I have an algorithm giving the list of all prime graphs on at most 8
vertices.
Best regards.
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