This contribution gives an extensive study on the Wiener indices, the number of closed walks, the coefficients of some graph polynomials (the adjacency polynomial, the Laplacian polynomial, the edge cover polynomial and the independence polynomial) of trees. Csikv?ri (2010) [4] introduced the generalized tree shift, which keeps the number of vertices of trees. Applying the generalized tree shifts and recurrence relation, we extend the works of Csikv?ri (2010) [4] and Csikv?ri (2013) [5]. Using a unified approach, we obtain the following main results: Firstly, for all n and 8, we characterize t...
