Dear Hojjat, Suppose G is a group and \Gamma is the graph you define in your message. The group Aut(G) has a natural action on G. Consider an orbit \Delta of this action. Then the complete graph on \Delta is a component of \Gamma. So, \Gamma is a union of complete graphs. So, it is enough to find the orbits of the automorphism group under its natural action on G. Up to isomorphism, the length of orbits is enough. I hope this helps you.
Regards, Alireza ----- Original Message ----- From: "hojjat Rostami" <rostamihoj...@yahoo.com> To: "forum@mail.gap-system.org" <fo...@gap-system.org> Sent: Saturday, August 8, 2015 1:26:11 PM Subject: [GAP Forum] Program for determining new graph 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 _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
