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## 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 |

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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)

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