| The spectral theory of graphs is a very dynamic area of graph theory research.By means of the research in algebraic theory skills and the basic knowledge of the graph theory,this research is the study of the eigenvalue of graph’s corresponding matrix.Their research have broad connection to combinatorial mathematics,analysis method,communication engineering and quantum chemistry discipline.The processing method about Taylor’s strongly regular graph research and Kro-necker’s product research,gave us more conditions to further study on the extrama of the Graph’s adjacent matrix eigenvalue.We discusses the relationship between the ad-jacent matrix eigenvalue of Taylor strong regular graph and the value of its order;the relationship between adjacent matrix eigenvalue of the graph who has another spectrum and its order,and the distribution of the graph eigenvalue,row sum,and the distribution of diagonal elements;the extrema of Nordhaus-Gaddum problem and Ky Fan k norm.The specific content is as follows:In chapter 1,we make an overview of the background and significance of the article topics,and also present the main result of this paper.In chapter 2,we discusses the relationship between the adjacent matrix eigenvalue of Taylor strong regular graph and the value of its order.In chapter 3,we discusses the relationship between adjacent matrix eigenvalue of the graph who has another spectrum and its order,and the distribution of the graph eigenvalue,row sum,and the distribution of diagonal elements;In chapter 4,we discusses the extrema of Nordhaus-Gaddum problem and Ky Fan k norm. |
