A Brief Introduction To Spectral Graph Theory
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A Brief Introduction To Spectral Graph Theory
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Author : Bogdan Nica
language : en
Publisher:
Release Date : 2018
A Brief Introduction To Spectral Graph Theory written by Bogdan Nica and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Eigenvalues categories.
"Spectral graph theory starts by associating matrices to graphs - notably, the adjacency matrix and the Laplacian matrix. The general theme is then, firstly, to compute or estimate the eigenvalues of such matrices, and secondly, to relate the eigenvalues to structural properties of graphs. As it turns out, the spectral perspective is a powerful tool. Some of its loveliest applications concern facts that are, in principle, purely graph theoretic or combinatorial. This text is an introduction to spectral graph theory, but it could also be seen as an invitation to algebraic graph theory. The first half is devoted to graphs, finite fields, and how they come together. This part provides an appealing motivation and context of the second, spectral, half. The text is enriched by many exercises and their solutions. The target audience are students from the upper undergraduate level onwards. We assume only a familiarity with linear algebra and basic group theory. Graph theory, finite fields, and character theory for abelian groups receive a concise overview and render the text essentially self-contained"--Back cover.
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.
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.
Spectral Graph Theory
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Author : Fan R. K. Chung
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Spectral Graph Theory written by Fan R. K. Chung and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
This text discusses spectral graph theory.
Algebraic Graph Theory
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Author : Chris Godsil
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Algebraic Graph Theory written by Chris Godsil 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 2013-12-01 with Mathematics categories.
This book presents and illustrates the main tools and ideas of algebraic graph theory, with a primary emphasis on current rather than classical topics. It is designed to offer self-contained treatment of the topic, with strong emphasis on concrete examples.
Topics In Algebraic Graph Theory
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Author : Lowell W. Beineke
language : en
Publisher: Cambridge University Press
Release Date : 2004-10-04
Topics In Algebraic Graph Theory written by Lowell W. Beineke 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 2004-10-04 with Mathematics categories.
There is no other book with such a wide scope of both areas of algebraic graph theory.
Quantum Probability And Spectral Analysis Of Graphs
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Author : Akihito Hora
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-05
Quantum Probability And Spectral Analysis Of Graphs written by Akihito Hora 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 2007-07-05 with Science categories.
This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.
Graph Energy
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Author : Xueliang Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-10
Graph Energy written by Xueliang Li 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 2012-08-10 with Mathematics categories.
This book is about graph energy. The authors have included many of the important results on graph energy, such as the complete solution to the conjecture on maximal energy of unicyclic graphs, the Wagner-Heuberger’s result on the energy of trees, the energy of random graphs or the approach to energy using singular values. It contains an extensive coverage of recent results and a gradual development of topics and the inclusion of complete proofs from most of the important recent results in the area. The latter fact makes it a valuable reference for researchers looking to get into the field of graph energy, further stimulating it with occasional inclusion of open problems. The book provides a comprehensive survey of all results and common proof methods obtained in this field with an extensive reference section. The book is aimed mainly towards mathematicians, both researchers and doctoral students, with interest in the field of mathematical chemistry.
Applying Graph Theory In Ecological Research
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Author : Mark R.T. Dale
language : en
Publisher: Cambridge University Press
Release Date : 2017-11-09
Applying Graph Theory In Ecological Research written by Mark R.T. Dale 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 2017-11-09 with Mathematics categories.
This book clearly describes the many applications of graph theory to ecological questions, providing instruction and encouragement to researchers.