You are here: Home / Shop / Product Detail Page |

## Lecture Notes in Mathematics #1915: Laplacian Eigenvectors of Graphs: Perron-Frobenius and Faber-Krahn Type Theorems (Softcover)"The volume investigates the structure of eigenvectors and looks at the number of their sign graphs ('nodal domains'), Perron components, graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology." — From the back cover ## $31.99 |

### Need More Info?

Please contact us if you've got questions about this product.## Condition

**GOOD:** The book’s front cover has a slight bend to it and some of the first few pages’ bottom corners have been creased, but the remainder of the book is in very good condition. Adding to its value is the fact that it is printed on acid-free paper.

## Description

From the back cover: “Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) ‘Geometric’ properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors.”

**BRIEF CONTENTS**

- 1 – Introduction
- 2 – Graph Laplacians
- 3 – Eigenfunctions and Nodal Domains
- 4 – Nodal Domain Theorems for Special Graph Classes
- 5 – Computational Experiments
- 6 – Faber-Krahn Type Inequalities
- A – Basic Notation
- B – Eigenfunctions Used in Figures
- C – List of Symbols
- References
- Index

About the series: “This series reports on new developments in mathematical research and teaching—quickly, informally and at a high level. The type of material considered for publication includes (1) Research monographs, (2) Lectures on a new field or presentation of a new angle in a classical field, and (3) Summer schools and intensive courses on topics of current research.” There have been at least 2090 volumes published since 1964 to the present.

## Details

- SKU:
- 1630
- Author:
- Biyikoğlu, Türker and Josef Leydold and Peter F. Stadler
- Publisher:
- Springer Science+Business Media
- Publish Date:
- 12 June 2011
- Format:
- Softcover
- Weight (pounds):
- 0.9
- Dimensions (W”xL”xH”):
- 8.3″x11.6″x0.4″
- ISBN-13:
- 9783540735090
- ISBN-10:
- 3540735097
- Series:
- Lecture Notes in Mathematics (LNM)

## Related Products

### Products related to "Lecture Notes in Mathematics #1915: Laplacian Eigenvectors of Graphs: Perron-Frobenius and Faber-Krahn Type Theorems (Softcover)"

- Views:

#### Encyclopedia of Mathematics and Its Applications 20: Finite Fields (Hardback)

$123.50

"In this book, which is the first one devoted entirely to finite fields, we have aimed at presenting both the classical and the applications-oriented aspect of the subject. Thus, in addition to what has to be considered the essential core of the theory, the reader will find results and techniques that are of importance mainly because of their use in applications." — From the Authors in the Preface

#### Encyclopedia of Mathematics and Its Applications 20: Finite Fields (Softcover)

$73.95

"In this book, which is the first one devoted entirely to finite fields, we have aimed at presenting both the classical and the applications-oriented aspect of the subject. Thus, in addition to what has to be considered the essential core of the theory, the reader will find results and techniques that are of importance mainly because of their use in applications." — From the Authors in the Preface

#### An Introduction to Random Matrices (Hardback)

$53.95

"The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic, and combinatorial). This diverse array of tools, while attesting to the vitality of the field, presents several formidable obstacles to the newcomer, and even to the expert probabilist. This rigorous introduction to the basic theory is sufficiently self-contained to be accessible to graduate students in mathematics or related sciences who have mastered probability theory at the graduate level, but who have not necessarily been exposed to advanced notions of functional analysis, algebra, or geometry." — From the back cover

#### Computer Graphics and Geometric Modeling: Mathematics (Hardback)

$12.49

"In addition to its use as a companion volume to computer graphics or geometric modeling courses, this volume would also make a good mathematics reference book, in particular for practitioners in the field of geometric modeling. Furthermore, because of its broad coverage and emphasis on explanation it could even be used as text for introductory mathematics courses on some of the covered topics, such as topology (general, combinatorial, algebraic, and differential) and geometry (differential and algebraic)." — From the back cover

#### Texts and Monographs in Computer Science: A Logical Approach to Discrete Math (Hardback)

$5.99

"Logic is the glue that binds together arguments and proofs in all domains. This text aims to teach the use of this fundamental and pervasive tool and exercise it thoroughly in applications that arise in computer science and mathematics." — From the back cover

#### Discrete Mathematics and Its Applications: Handbook of Computational Group Theory (Hardback)

$79.99

"The origins of computational group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics." — From the back cover

#### Iterative Methods for Sparse Linear Systems, Second Edition (Softcover)

$73.95

"This book can be used to teach graduate-level courses on iterative methods for linear systems. Engineers and mathematicians will find its contents easily accessible, and practitioners and educators will value it as a helpful resource. The preface includes syllabi that can be used for either a semester- or quarter-length course in both mathematics and computer science." — From the back cover

#### Discrete Mathematics and Its Applications: A Combinatorial Approach to Matrix Theory and Its Applications (Hardback)

$73.75

"Unlike most elementary books on matrices,

**A Combinatorial Approach to Matrix Theory and Its Applications**employs combinatorial and graph-theoretical tools to develop basic theorems of matrix theory, shedding new light on the subject by exploring the connections of these tools to matrices." — From the back cover#### Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry (Hardback)

$58.59

"Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications." — From the back cover

#### Encyclopedia of Mathematics and Its Applications 94: Mathematical Constants (Hardback)

$47.39

"The pages of

*Mathematical Constants*abound in thousands of tales about numbers. This book is an amazing piece of erudition destined to fascinate the novice, puzzle the exerpt, and trigger the imagination of all." — the late Philippe Flajolet, renowned computer scientist#### Polyhedra (Softcover)

$45.99

"Polyhedra have cropped up in many different guises throughout recorded history. In modern times, polyhedra and their symmetries have been cast in a new light by combinatorics and group theory." — From the back cover

#### Graduate Texts in Mathematics: A Course in Arithmetic (Hardback)

$40.95

This book is divided into two parts: the first is purely algebraic, while the second uses "analytic" methods (holomorphic functions).

#### Conceptual Mathematics: A First Introduction to Categories, Second Edition (Softcover)

$39.89

"In the last sixty years, the use of the notion of category has led to a remarkable unification and simplification of mathematics.

*Conceptual Mathematics*introduces this tool for the learning, development, and use of mathematics, to beginning students and also to practising mathematical scientists." — From the back cover#### Student Mathematical Library, Volume 46: Lectures on Surfaces: (Almost) Everything You Wanted to Know about Them (Softcover)

$39.59

"The assumed background is the standard calculus sequence, some linear algebra, and rudiments of ODE and real analysis. All notions are introduced and discussed, and virtually all results proved, based on this background." — From the back cover

#### Handbook of Mathematics and Computational Science (Hardback)

$39.50

"The Harris and Stocker Handbook of Mathematics and Computation Science is a complete desk-top reference for working scientists, engineers, and students. It serves as a veritable math toolbox for rapid access to a wealth of mathematics information for everyday use in problem solving, homework, examinations, etc." — From the back cover

#### Complex Functions: An Algebraic and Geometric Viewpoint (Softcover)

$38.65

"This book is based on lectures given to advance undergraduates and is well-suited as a textbook for a second course in complex function theory. Professionals will also find it valuable as a straightforward introduction to a subject which is finding widespread application throughout mathematics." — From the back cover

#### Clifford Algebras with Numeric and Symbolic Computations (Hardback)

$37.99

"This new book is an excellent resource for those mathematicians, physicists, engineers, and scientific computing researchers who currently use Clifford algebra methods in their investigations. It is also appealing to those who would like to quickly become familiar with the theory and computational practice in some of the most recent and fascinating applications of Clifford algebras." — From the back cover

#### The Classical Groups: Their Invariants and Representations, Second Edition (Softcover) [2142]

$37.99

This book belongs to the

**Princeton Landmarks in Mathematics**series, which consists of books "written by some of the world's finest scientists on topics of lasting importance. These books will become indispensable additions to the personal libraries of advanced students, teaching faculty, and professional mathematicians." — Taken from the back cover#### Combinatorial Optimization (Hardback)

$37.95

This textbook is "a complete, highly accessible introduction to one of today's most exciting areas of applied mathematics." — From the back cover

#### Undergraduate Texts in Mathematics: Geometric Constructions (Hardback)

$36.25

"Geometric constructions have been a popular part of mathematics throughout history. The ancient Greeks made the subject an art, which was enriched by the medieval Arabs, but which required the algebra of the Renaissance for a thorough understanding. Through coordinate geometry, various geometric construction tools can be associated with various fields of real numbers. This book is about these associations." — From the back cover