Let f be a continuous mapping from tree (i. e. compact connected one-dimensional branched manifold without cycles) with e endpoints to itself, and n a natural number. In this paper, we introduce the definitions of n-specification property (i.e. , n-SP) and quasi-speci-fication property (i. e. QSP), and show that f is topological mixing if and only if f has 2λ(e-1)! -SP (or QSP), where λ= min{e -2,1}. |