Abstract: Let A be a basic,connected finite dimensional algebra over an algebraically closed field with finite representation type, α(A) be the maximum of set consisting of numbers of indecomposable summands in the middle term of Auslander Reiten sequences in mod A. In this paper we show that if α(A)=1, then Γ A contains oriented cycles if and only if Γ A contains DT r periodic modules. When α(A) we give counterexamples to the assertion. 

Key words: Auslander-Reiten quiver, Auslander-Reiten sequences, oriented cycles, DT-r periodic molules