An Introduction to the Theory of Graph Spectra

This introductory text explores the theory of graph spectra: a topic with applications across a wide range of subjects, including computer science, quantum chemistry and electrical engineering. The spectra examined here are those of the adjacency matrix, the Seidel matrix, the Laplacian, the normalized Laplacian and the signless Laplacian of a finite simple graph. The underlying theme of the book is the relation between the eigenvalues and structure of a graph. Designed as an introductory text for graduate students, or anyone using the theory of graph spectra, this self-contained treatment assumes only a little knowledge of graph theory and linear algebra. The authors include many developments in the field which arise as a result of rapidly expanding interest in the area. Exercises, spectral data and proofs of required results are also provided. The end-of-chapter notes serve as a practical guide to the extensive bibliography of over 500 items.

Preface; 1. Introduction; 2. Graph operations and modifications; 3. Spectrum and structure; 4. Characterizations by spectra; 5. Structure and one eigenvalue; 6. Spectral techniques; 7. Laplacians; 8. Additional topics; 9. Applications; Appendix; Bibliography; Index of symbols; Index.

This is an introductory text for graduate students, or anyone using the theory of graph spectra, that assumes only a little knowledge of graph theory and linear algebra. The authors include developments in the field, exercises, spectral data, detailed proofs and an extensive bibliography.

Dragoš Cvetkovic is Professor in the Mathematical Institute at the Serbian Academy of Sciences and Arts, Belgrade.
Peter Rowlinson is Emeritus Professor of Mathematics in the Department of Computing Science and Mathematics at the University of Stirling.
Slobodan Simic is Full Research Professor in the Mathematical Institute at the Serbian Academy of Sciences and Arts, Belgrade.