Spectral Characterization Of Several Classes Of Graphs

As an important part of algebraic graph theory, spectral graph theory mainly concerns with the adjacency spectrum and Laplacian spectrum of a graph. A graph is said to be deter-mined by its adjacency spectrum (resp., Laplacian spectrum) if there is no other nonisomorphic graph with the same adjacency spectrum (resp., Laplacian spectrum).There are five chapters in this thesis. The background and development of the spectral determined problem will be introduced in chapter 1; in chapter 2, we will present some basic definitions and results which will be used in the following chapters; in chapter 3, we will show that graphsθ(m, m, m) andθ'(m, m, m) are determined by their Laplacian spectrum; in chapter 4, we will investigate the spectral determined problem of a class of bicyclic graphs Cm,n; in chapter 5, we will discuss whether graph Hp,2 is determined by its adjacency or Laplacian spectrum.