On The Spectral Radius Of Trees

In this paper, we mainly study the spectral radius of trees which is the important and special branch of graph theory. There are already many theories and techniques in this field. Furthermore we discuss the spectral radius of trees with fixed maximal degree and give the upper bound of the spectral radius of these trees respectively. Secondly we discuss some trees with bigger spectral radius. By analyzing its structure we find the relationships between spectral radius of trees and its maximal degree. Then we give the ordering of spectral radius of trees.1. We give the extreme trees with fixed number of vertices and fixed maximal degree, and estimate the upper bound and lower bound of the spectral radius of those trees respectively. Those results will be better than former results.2. We give ordering of spectral radius of trees. Furthermore we give the trees with 13th spectral radius to 32rd spectral radius. Finally we give a new upper bound of the spectral radius of trees.