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The power graph of a group is the graph whose vertex set is the set ofnontrivial elements of group, two elements being adjacent if one is a power ofthe other. We introduce some way for find the automorphism groups of somegraphs. As an application We describe the full automorphism group of the powergraph of all finite groups. Also we obtain the full automorphism group of powergraph of abelian, homocyclic and nilpotent groups

A description of automorphism group of power graphs of finite groups