Spectral Radius And Algebraic Connectivity Of Some Graphs

The study of graph spectra is an important direction of research in algebraic graph theory, and its main object of study is the adjacency spectrum and the Laplacian spectrum. This direction of research associates the graph in graph theory with the matrix in algebra by the matrix representation of a graph, then studies the algebraic property of graphs with the methods in graph theory and algebra.Brualdi-Solheid problem is a very important problem in the research of graph spectrum. So far the results related to this problem have been so much, but the problem is not fully resolved. This thesis will proceed with the research of this problem. The main content can be divided into three chapters. The first chapter gives an overview of graph spectrum, introduces the related definitions and notations, and explains the structure of this thesis.The second chapter studies the spectral radius of unicyclic graphs given order and edge independence number, the spectral radius of bicyclic graphs.The third chapter orders the trees by their algebraic connectivity, and determines all the trees of order no less than 45 with algebraic connectivity in the interval .