A Graph With Three Different Q Eigenvalues

In spectra of graphs theory, the spectrum and eigenvalues of graphs decide to some basic properties and structure of graphs, the relationship of adjacency ma-trix、eigenvalues and its maximum eigenvalue corresponding eigenvector of graphs provide a new method for the study of graphs which has three distinct eigenvaluesThis paper focus on the study of graphs which has three distinct Q eigenvalues based on the relationship of Q matrix、Q eigenvalues and its maximum Q eigenvalue corresponding eigenvector of graphs.The construction of chapters and the concrete contents of this paper are as follows:Chapter1:Preliminaries. This chapter presents the paper will use of some basic concepts and the related conclusion figure:The base concept of graphs, Q spectrum and some basic properties, the union of the graphs.Chapter2:Q eigenvalue properties of connected graph. The first,this chapter gives the basic nature of the Q spectrum properties of connected graph. The second, it gives basic properties and lemma of connected graph which has three distinct Q eigenvalues.Chapter3:Connected graphs with three different Q eigenvalue. This chapter applying basic properties of connected graphs which has three distinct Q eigenvalue, obtain strongly regular graphs、bipartite graphs、biregular graphs and cones with three different Q eigenvalue.Chapter4:Not connected graph With three different Q eigenvalue. This chapter using the definition of polynomials and union of graphs, get some not connected (?)...