In the graph you define, two elements are adjacent if they lie in the same orbit of the automorphism group. So one way to construct it is

aut := AutomorphismGroup ( G );
adj := function  (x,y)
 return x in Orbit (aut, y);
end;
Graph (aut, Elements (G), OnPoints, adj);

Regards,
Sven Reichard.


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Am 8. August 2015 11:09:25 schrieb hojjat Rostami <rostamihoj...@yahoo.com>:

Dear forum,
Can someone help with the construction a graph for a group G, where its vertices set is G and two element x,y of G are connected if there exists  some automorphism a such that a(x)=y or a(y)=x.Best regard
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