Transitivity on graphs is a concept widely investigated. This suggest to analyze the action of automorphisms on other sets. In this paper, we study the action on the family of γ-sets (minimum dominating sets), the graph is called γ-transitive if given two γ-sets there exists an automorphism which maps one onto the other. We deal with two families: paths Pn and cycles Cn. Their γ-sets are fully characterized and the action of the automorphism group on the family of γ-sets is fully analyzed.
