Maximum Degree, Independence Number And Spectral Radius Of A Graph

The spectral radius of a graph is the largest eigenvalue of the adjacency matrix of the graph. An important direction of spectral theory is studying the relation between the spectral radius and the structure of graphs. This thesis concerns characterizing the graphs with minimum spectral radius among the graphs with some given parameters and is divided into three chapters.In Chapter one, we introduce research background and some notations. In Chapter two, we determine the trees with minimum spectral radius among the trees with maximum degree3(respectively,4) and the number of vertices with maximum degree more than3(respectively, no more than3), when the order of the trees is large enough. In the last chapter, we characterize the graphs with min-imum spectral radius among the connected graphs of order n with independence number3(respectively,4) and n=3k(k>15)(respectively, n=4κ(κ≥26)).