Locating Eigenvalues in Graphs
Springer International Publishing (Verlag)
978-3-031-11697-1 (ISBN)
Studies in spectral graph theory seek to determine properties of a graph through matrices associated with it. It turns out that eigenvalues and eigenvectors have surprisingly many connections with the structure of a graph. This book approaches this subject under the perspective of eigenvalue location algorithms. These are algorithms that, given a symmetric graph matrix M and a real interval I, return the number of eigenvalues of M that lie in I. Since the algorithms described here are typically very fast, they allow one to quickly approximate the value of any eigenvalue, which is a basic step in most applications of spectral graph theory. Moreover, these algorithms are convenient theoretical tools for proving bounds on eigenvalues and their multiplicities, which was quite useful to solve longstanding open problems in the area. This book brings these algorithms together, revealing how similar they are in spirit, and presents some of their main applications.
This work can be of special interest to graduate students and researchers in spectral graph theory, and to any mathematician who wishes to know more about eigenvalues associated with graphs. It can also serve as a compact textbook for short courses on the topic.
Carlos Hoppen holds a PhD in Combinatorics and Optimization from the University of Waterloo, Canada. He is an Associate Professor of Mathematics at the Federal University of Rio Grande do Sul (UFRGS), Brazil. His research focuses on probabilistic and extremal combinatorics, and spectral graph theory. David P. Jacobs is a Professor Emeritus of Computer Science at Clemson University, USA. He has done research in various areas including graph algorithms and spectral graph theory. In 2006, he visited UFRGS as a Fulbright Scholar. Vilmar Trevisan is a Professor of Mathematics at UFRGS. He earned a PhD in Mathematics at Kent State University, USA. His research focuses on combinatorics and spectral graph theory. He is currently a Visiting Professor at the Universita degli Studi di Napoli, Italy.
Preface.- Introduction.- Preliminaries.- Locating Eigenvalues in Trees.- Graph Representations.- Locating Eigenvalues in Threshold Graphs and Cographs.- Locating Eigenvalues in Arbitrary Graphs.- Locating Eigenvalues in Distance Hereditary Graphs.- Some Other Algorithms.- References.
"The book is well structured, and gives the necessary background, detailed insight into eigenvalue location algorithms as well as their applications and possible relations with some open problems. It provides a concise and at the same time rich introduction to eigenvalue location algorithms." (Milica Andelic, zbMATH 1511.05001, 2023)
“The book is well structured, and gives the necessary background, detailed insight into eigenvalue location algorithms as well as their applications and possible relations with some open problems. It provides a concise and at the same time rich introduction to eigenvalue location algorithms.” (Milica Andelić, zbMATH 1511.05001, 2023)
| Erscheinungsdatum | 24.09.2022 |
|---|---|
| Reihe/Serie | SpringerBriefs in Mathematics |
| Zusatzinfo | XII, 136 p. 37 illus., 25 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 235 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Graphentheorie | |
| Schlagworte | Adjacency Matrix • eigenvalue • Graph • Graph Algorithms • Laplacian matrix • linear-time algorithm • Spectral Graph theory • spectrum • Tree |
| ISBN-10 | 3-031-11697-6 / 3031116976 |
| ISBN-13 | 978-3-031-11697-1 / 9783031116971 |
| Zustand | Neuware |
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