Locating eigenvalues in graphs : algorithms and applications / Carlos Hoppen, David P. Jacobs, Vilmar Trevisan.
2022
QA193
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Title
Locating eigenvalues in graphs : algorithms and applications / Carlos Hoppen, David P. Jacobs, Vilmar Trevisan.
Author
Hoppen, Carlos, author.
ISBN
9783031116988 (electronic bk.)
3031116984 (electronic bk.)
9783031116971
3031116976
3031116984 (electronic bk.)
9783031116971
3031116976
Published
Cham : Springer, [2022]
Copyright
©2022
Language
English
Description
1 online resource (xii, 136 pages) : illustrations (some color).
Item Number
10.1007/978-3-031-11698-8 doi
Call Number
QA193
Dewey Decimal Classification
512.9/436
Summary
This book focuses on linear time eigenvalue location algorithms for graphs. This subject relates to spectral graph theory, a field that combines tools and concepts of linear algebra and combinatorics, with applications ranging from image processing and data analysis to molecular descriptors and random walks. It has attracted a lot of attention and has since emerged as an area on its own. 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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed October 4, 2022).
Added Author
Jacobs, David P., author.
Trevisan, Vilmar, author.
Trevisan, Vilmar, author.
Series
SpringerBriefs in mathematics. 2191-8201
Available in Other Form
Print version: 9783031116971
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Table of Contents
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.
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.