Laplacian Eigenvectors of Graphs

There are many applications and results on graph Laplacian eigenvalues and their relations to numerous graph invariants, ... maximum cut, clustering, graph partition), and approximations for optimization problems on graphs (cutwidth, ...

Laplacian Eigenvectors of Graphs

This fascinating volume investigates the structure of eigenvectors and looks at the number of their sign graphs ("nodal domains"), Perron components, and graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology. Eigenvectors of graph Laplacians may seem a surprising topic for a book, but the authors show that there are subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs.

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Laplacian Eigenvectors of Graphs
Language: en
Pages: 120
Authors: Türker Biyikoglu, Josef Leydold, Peter F. Stadler
Categories: Mathematics
Type: BOOK - Published: 2007-07-07 - Publisher: Springer

This fascinating volume investigates the structure of eigenvectors and looks at the number of their sign graphs ("nodal domains"), Perron components, and graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology. Eigenvectors of graph Laplacians may seem a surprising topic
The Classification of Countable Homogeneous Directed Graphs and Countable Homogeneous $n$-tournaments
Language: en
Pages: 161
Authors: Gregory L. Cherlin
Categories: Mathematics
Type: BOOK - Published: 1998 - Publisher: American Mathematical Soc.

In this book, Ramsey theoretic methods introduced by Lachlan are applied to classify the countable homogeneous directed graphs. This is an uncountable collection, and this book presents the first explicit classification result covering an uncountable family. The author's aim is to demonstrate the potential of Lachlan's method for systematic use.
Graphs of Groups on Surfaces
Language: en
Pages: 378
Authors: A.T. White
Categories: Mathematics
Type: BOOK - Published: 2001-04-27 - Publisher: Elsevier

The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups of both graphs and maps are studied. In addition connections
Handbook of Product Graphs
Language: en
Pages: 536
Authors: Richard Hammack, Wilfried Imrich, Sandi Klavžar
Categories: Computers
Type: BOOK - Published: 2011-06-06 - Publisher: CRC Press

Handbook of Product Graphs, Second Edition examines the dichotomy between the structure of products and their subgraphs. It also features the design of efficient algorithms that recognize products and their subgraphs and explores the relationship between graph parameters of the product and factors. Extensively revised and expanded, the handbook pre
Graphs from Rings
Language: en
Pages: 538
Authors: David F. Anderson, T. Asir, Ayman Badawi, T. Tamizh Chelvam
Categories: Mathematics
Type: BOOK - Published: 2021-12-02 - Publisher: Springer Nature

This book gives an overview of research on graphs associated with commutative rings. The study of the connections between algebraic structures and certain graphs, especially finite groups and their Cayley graphs, is a classical subject which has attracted a lot of interest. More recently, attention has focused on graphs constructed