The Spectral Radius Of The Complement Of Some Graphs

In the graphs theory, people introduce various matrices, such as the adjacency matrix,the distance matrix, the Laplacian matrix, the signless Laplacian matrix and so on, to re-search the properties of graphs by studying the algebraic properties of matrices.The matrices that people most usually study are adjacency matrix, Laplacian matrix andsignless Laplacian matrix. Comparing with adjacency matrix, Laplacian matrix and signlessLaplacian matrix contain the information about the degree of all vertices. It can show someproperties of graphs well. This thesis will research the problems of signless Laplacian matrixand adjacency matrix. The main content can be divided into four sections:In the first section, we gives the research background and development of spectral ra-dius, Laplacian spectral radius and signless Laplacian spectral radius.In the second section, we study the signless Laplacian spectral radius of the complementof graphs, and also get the graph which attains the maximum spectral radius.In the third section, we study the spectral radius of the complement of bicyclic graph,and also get the graph which attains the maximum spectral radius.In the fourth section, we study the signless Laplacian spectral radius of bicyclic graphswith k pendant vertices, and also get the graph which attains the maximum spectral radius.