[GAP Forum] Program for determining new graph

[arashrafi at kashanu.ac.ir]

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" <rostamihojjat at yahoo.com>
To: "forum at mail.gap-system.org" <forum at 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
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