Spectral Radius Of Graphs
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Spectral Radius Of Graphs
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Author : Dragan Stevanovic
language : en
Publisher: Academic Press
Release Date : 2014-10-13
Spectral Radius Of Graphs written by Dragan Stevanovic and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-13 with Mathematics categories.
Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the book delves deeper into the properties of the principal eigenvector; a critical subject as many of the results on the spectral radius of graphs rely on the properties of the principal eigenvector for their proofs. A following chapter surveys spectral radius of special graphs, covering multipartite graphs, non-regular graphs, planar graphs, threshold graphs, and others. Finally, the work explores results on the structure of graphs having extreme spectral radius in classes of graphs defined by fixing the value of a particular, integer-valued graph invariant, such as: the diameter, the radius, the domination number, the matching number, the clique number, the independence number, the chromatic number or the sequence of vertex degrees. Throughout, the text includes the valuable addition of proofs to accompany the majority of presented results. This enables the reader to learn tricks of the trade and easily see if some of the techniques apply to a current research problem, without having to spend time on searching for the original articles. The book also contains a handful of open problems on the topic that might provide initiative for the reader's research. - Dedicated coverage to one of the most prominent graph eigenvalues - Proofs and open problems included for further study - Overview of classical topics such as spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem
The Joint Spectral Radius
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Author : Raphaël Jungers
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-19
The Joint Spectral Radius written by Raphaël Jungers and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-19 with Technology & Engineering categories.
This monograph is based on the Ph.D. Thesis of the author [58]. Its goal is twofold: First, it presents most researchwork that has been done during his Ph.D., or at least the part of the work that is related with the joint spectral radius. This work was concerned with theoretical developments (part I) as well as the study of some applications (part II). As a second goal, it was the author’s feeling that a survey on the state of the art on the joint spectral radius was really missing in the literature, so that the ?rst two chapters of part I present such a survey. The other chapters mainly report personal research, except Chapter 5 which presents animportantapplicationofthejointspectralradius:thecontinuityofwavelet functions. The ?rst part of this monograph is dedicated to theoretical results. The ?rst two chapters present the above mentioned survey on the joint spectral radius. Its minimum-growth counterpart, the joint spectral subradius, is also considered. The next two chapters point out two speci?c theoretical topics, that are important in practical applications: the particular case of nonne- tive matrices, and the Finiteness Property. The second part considers applications involving the joint spectral radius.
An Introduction To The Theory Of Graph Spectra
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Author : Dragoš Cvetković
language : en
Publisher: Cambridge University Press
Release Date : 2009-10-15
An Introduction To The Theory Of Graph Spectra written by Dragoš Cvetković and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-15 with Mathematics categories.
This introductory text explores the theory of graph spectra: a topic with applications across a wide range of subjects, including computer science, quantum chemistry and electrical engineering. The spectra examined here are those of the adjacency matrix, the Seidel matrix, the Laplacian, the normalized Laplacian and the signless Laplacian of a finite simple graph. The underlying theme of the book is the relation between the eigenvalues and structure of a graph. Designed as an introductory text for graduate students, or anyone using the theory of graph spectra, this self-contained treatment assumes only a little knowledge of graph theory and linear algebra. The authors include many new developments in the field which arise as a result of rapidly expanding interest in the area. Exercises, spectral data and proofs of required results are also provided. The end-of-chapter notes serve as a practical guide to the extensive bibliography of over 500 items.
The Minimal Spectral Radius Of Graphs With A Given Diameter
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Author : E.R. van Dam
language : en
Publisher:
Release Date : 2006
The Minimal Spectral Radius Of Graphs With A Given Diameter written by E.R. van Dam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Spectra Of Graphs
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Author : Andries E. Brouwer
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-17
Spectra Of Graphs written by Andries E. Brouwer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-17 with Mathematics categories.
This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text. Spectra of Graphs is written for researchers, teachers and graduate students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theorem and eigenvalue interlacing are included.
Graphs And Matrices
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Author : Ravindra B. Bapat
language : en
Publisher: Springer
Release Date : 2014-09-19
Graphs And Matrices written by Ravindra B. Bapat and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-19 with Mathematics categories.
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.
Eigenspaces Of Graphs
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Author : Dragoš M. Cvetković
language : en
Publisher: Cambridge University Press
Release Date : 1997-01-09
Eigenspaces Of Graphs written by Dragoš M. Cvetković and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-09 with Mathematics categories.
Current research on the spectral theory of finite graphs may be seen as part of a wider effort to forge closer links between algebra and combinatorics (in particular between linear algebra and graph theory).This book describes how this topic can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. The extension of spectral techniques proceeds at three levels: using eigenvectors associated with an arbitrary labelling of graph vertices, using geometrical invariants of eigenspaces such as graph angles and main angles, and introducing certain kinds of canonical eigenvectors by means of star partitions and star bases. One objective is to describe graphs by algebraic means as far as possible, and the book discusses the Ulam reconstruction conjecture and the graph isomorphism problem in this context. Further problems of graph reconstruction and identification are used to illustrate the importance of graph angles and star partitions in relation to graph structure. Specialists in graph theory will welcome this treatment of important new research.
Spectral Algorithms
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Author : Ravindran Kannan
language : en
Publisher: Now Publishers Inc
Release Date : 2009
Spectral Algorithms written by Ravindran Kannan and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Computers categories.
Spectral methods refer to the use of eigenvalues, eigenvectors, singular values and singular vectors. They are widely used in Engineering, Applied Mathematics and Statistics. More recently, spectral methods have found numerous applications in Computer Science to "discrete" as well "continuous" problems. Spectral Algorithms describes modern applications of spectral methods, and novel algorithms for estimating spectral parameters. The first part of the book presents applications of spectral methods to problems from a variety of topics including combinatorial optimization, learning and clustering. The second part of the book is motivated by efficiency considerations. A feature of many modern applications is the massive amount of input data. While sophisticated algorithms for matrix computations have been developed over a century, a more recent development is algorithms based on "sampling on the y" from massive matrices. Good estimates of singular values and low rank approximations of the whole matrix can be provably derived from a sample. The main emphasis in the second part of the book is to present these sampling methods with rigorous error bounds. It also presents recent extensions of spectral methods from matrices to tensors and their applications to some combinatorial optimization problems.
Introduction To Random Graphs
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Author : Alan Frieze
language : en
Publisher: Cambridge University Press
Release Date : 2016
Introduction To Random Graphs written by Alan Frieze and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.
The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.
Mathematical Programming And Game Theory
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Author : S.K. Neogy
language : en
Publisher: Springer
Release Date : 2018-11-28
Mathematical Programming And Game Theory written by S.K. Neogy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-28 with Mathematics categories.
This book discusses recent developments in mathematical programming and game theory, and the application of several mathematical models to problems in finance, games, economics and graph theory. All contributing authors are eminent researchers in their respective fields, from across the world. This book contains a collection of selected papers presented at the 2017 Symposium on Mathematical Programming and Game Theory at New Delhi during 9–11 January 2017. Researchers, professionals and graduate students will find the book an essential resource for current work in mathematical programming, game theory and their applications in finance, economics and graph theory. The symposium provides a forum for new developments and applications of mathematical programming and game theory as well as an excellent opportunity to disseminate the latest major achievements and to explore new directions and perspectives.