Spectral Radius Of Some Kinds Of Graphs

In this paper, we mainly study the spectrum of simple connected undirected graphs, including the adjacency spectrum and the Laplace spectrum. Some results will be given in this thesis.1. By using the improved method of graft transformation, we characterize the 2-trees that maximize the second and the third largest adjacency spectral radius.2. We study the graphs with diameter 2 and one class of their subgraphs and characterize the extremal graphs whose adjacency spectral radius is the largest in these two classes, respectively. Moreover, we get the upper bounds for the spectral radii of these extremal graphs.3. By using the inequalities on the sum of the squares of the degrees of a graph, we get a sharp upper bound for the Laplace spectral radius of simple connected undirected graphs:equality holds if and only if G is star graph K_1,(n-1).