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Graphs with Few Eigenvalues

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Graphs with Few Eigenvalues
论文目录
 
Acknowledgements第1-8页
Abstract第8-12页
1 Introduction第12-24页
  1.1 Graphs with few eigenvalues第14-19页
    1.1.1 Graphs with few A-eigenvalues第14-16页
    1.1.2 Graphs with few S-eigenvalues第16-17页
    1.1.3 Graphs with few generalized adjacency eigenvalues第17-18页
    1.1.4 Graphs with few D-eigenvalues第18页
    1.1.5 Other matrices第18-19页
  1.2 Spectral characterization of graphs第19-22页
    1.2.1 Adjacency matrix第19-20页
    1.2.2 Seidel, Laplacian and signless Laplacian matrices第20页
    1.2.3 Computer results第20-21页
    1.2.4 Cospectrality and generalized adjacency matrices第21-22页
    1.2.5 Distance matrix第22页
  1.3 Summary of the main results第22-24页
2 Preliminaries第24-32页
  2.1 Graphs第24-25页
  2.2 Matrices第25-27页
  2.3 Interlacing and equitable partitions第27-29页
  2.4 Generalized adjacency matrices第29-32页
    2.4.1 Graphs with two generalized adjacency eigenvalues第29-32页
3 Graphs with few main and plain A-eigenvalues第32-52页
  3.1 The main-plain index and the refined spectrum第32-34页
  3.2 Graphs with few main A-eigenvalues第34-44页
    3.2.1 Introduction第34-36页
    3.2.2 Equitable graphs第36-38页
    3.2.3 Graphs with two S-eigenvalues第38-41页
    3.2.4 Constructions第41-44页
  3.3 Graphs with few main and plain A-eigenvalues第44-52页
    3.3.1 Introduction第44-45页
    3.3.2 Characterizations第45-47页
    3.3.3 Examples and discussion第47-52页
4 Graph with three generalized adjacency eigenvalues第52-60页
  4.1 Introduction第52-53页
  4.2 Regular two-graphs第53-55页
  4.3 Cones over strongly regular graphs第55-57页
  4.4 Constructions第57-60页
5 Distance spectra of graphs第60-68页
  5.1 Introduction第60-61页
  5.2 Bounds on D-eigenvalues of graphs第61-63页
  5.3 Graphs with three D-eigenvalues第63-65页
  5.4 Distance spectral characterization of hypercubes第65-68页
6 Future work第68-72页
  6.1 Adjacency matrix第68-69页
  6.2 Seidel matrix第69-70页
  6.3 Generalized adjacency matrices第70页
  6.4 Distance matrix第70-72页
References第72-78页
Research work conducted during PhD第78页

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