The Spectral Radius Of Trees With Minor Matching Number

Graph theory is a mathematical discipline with a long history.In recent 30 years,as the development of computer technology,the application of graph theory is more and more extensive.Spectrum theory is an important topic in algebraic graph theory,which mainly research the eigenvectors and characteristics of graph matrix by using the methods of matrix theory,linear algebra and so on.This paper basises on the existing research results and focus on the minimal spectral radius of trees with minor matching number.The main contents are as follows:The first chapter mainly generalizes the development of graph theory and spectrum theory,introduces the article structure and some common concepts and symbols.The second chapter is based on existing results,by using methods such as graft transformation,characteristic polynomial comparison,direct calculation,we confirms the spectral radius of trees on n k+3(k3) vertices which matching number is =2, 3, 4and find the tree with minimal spectral radius.