Abstract: Let G be a 2-tree with n vertices. By applying the technique of edge moving transformation, we first obtained a decidable theorem about the spectral radius of G. Then through comparing the characteristic polynomials of some graphs, the extremal graphs which have the fourth and fifth largest spectral
radii of this kind of graphs were determined.

Key words: spectral radius, Perron vector, 2-trees, spectral radius, Perron vector