On The Minimal Spectral Radius Of Trees With A Given Diameter

In this paper,we mainly study the spectral radius of trees which is the important and special topic of graph theory.There are already many theories and techniques in this field.Furthermore we discuss the minimal spectral radius of trees with a fixed diameter and trees with minimal spectral radii. Main results are as follows.1.We give the extreme trees with the minimal spectra radius when the diameter d=1,2,3,4,and calculate the value of this spectra radius.2.For the diameter d=n-4,n-3,n-2,n-1,trees with minimal spectral radius are characterized.