Inequalities for Graph Eigenvalues
Seiten
2015
Cambridge University Press (Verlag)
978-1-107-54597-7 (ISBN)
Cambridge University Press (Verlag)
978-1-107-54597-7 (ISBN)
Written for mathematicians working with the theory of graph spectra, this book explores more than 400 inequalities for eigenvalues of the six matrices associated with graphs. It presents the main results and then details their proofs, discussions, comparisons, examples, and exercises. Open problems and pointers to the literature are provided.
Written for mathematicians working with the theory of graph spectra, this book explores more than 400 inequalities for eigenvalues of the six matrices associated with finite simple graphs: the adjacency matrix, Laplacian matrix, signless Laplacian matrix, normalized Laplacian matrix, Seidel matrix, and distance matrix. The book begins with a brief survey of the main results and selected applications to related topics, including chemistry, physics, biology, computer science, and control theory. The author then proceeds to detail proofs, discussions, comparisons, examples, and exercises. Each chapter ends with a brief survey of further results. The author also points to open problems and gives ideas for further reading.
Written for mathematicians working with the theory of graph spectra, this book explores more than 400 inequalities for eigenvalues of the six matrices associated with finite simple graphs: the adjacency matrix, Laplacian matrix, signless Laplacian matrix, normalized Laplacian matrix, Seidel matrix, and distance matrix. The book begins with a brief survey of the main results and selected applications to related topics, including chemistry, physics, biology, computer science, and control theory. The author then proceeds to detail proofs, discussions, comparisons, examples, and exercises. Each chapter ends with a brief survey of further results. The author also points to open problems and gives ideas for further reading.
Zoran Stanić is Assistant Professor in the Faculty of Mathematics at the University of Belgrade. He has published around 40 scientific papers. His current research interests are algebraic graph theory, numerical mathematics, and computer science.
Preface; 1. Introduction; 2. Spectral radius; 3. Least eigenvalue; 4. Second largest eigenvalue; 5. Other eigenvalues of the adjacency matrix; 6. Laplacian eigenvalues; 7. Signless Laplacian eigenvalues; 8. Inequalities for multiple eigenvalues; 9. Other spectra of graphs; References; Inequalities; Subject index.
| Reihe/Serie | London Mathematical Society Lecture Note Series |
|---|---|
| Zusatzinfo | Worked examples or Exercises; 7 Tables, black and white; 35 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 152 x 229 mm |
| Gewicht | 420 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Graphentheorie |
| ISBN-10 | 1-107-54597-8 / 1107545978 |
| ISBN-13 | 978-1-107-54597-7 / 9781107545977 |
| Zustand | Neuware |
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