The Minimal Spectral Radius Of Trees With Fixed Matching Number

As an independent discipline of the Spectral of graphs have their special researchmethods. We commonly use the several methods in the Special of graph, such as algebramethod, matrix theory method and graph mathematical operation method. The tree is a classof common and special graph. Compared with the minimal spectral radius of trees, there areso many research results about the largest spectral radius of trees.In this paper, we mainly study the minimal spectral radius of trees in graph theory.Let R denote the set of trees on n k1(k2)vertices with fixed number. Furthermorewe discuss the minimal spectral radius of trees and trees in R. The paper will be arranged asfollowing:1. The first chapter introduce the general outline of the graph and the spectrum theory,related concepts and notations, and explain the structure of this paper.2. The second chapter first give the minimal spectral radius inR2、R3.3. The third chapter give the give the minimal spectral radius inR4. First we give therelation of the maximum degree and the spectral radius inR4, and then give the minimalspectral radius of trees inR4.