Distribution Of Laplacian Eigenvalues Of Graphs
DOWNLOAD
Download Distribution Of Laplacian Eigenvalues Of Graphs PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Distribution Of Laplacian Eigenvalues Of Graphs book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Distribution Of Laplacian Eigenvalues Of Graphs
DOWNLOAD
Author : Bilal Ahmad Rather
language : en
Publisher: A.K. Publications
Release Date : 2022-12-22
Distribution Of Laplacian Eigenvalues Of Graphs written by Bilal Ahmad Rather and has been published by A.K. Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-22 with Mathematics categories.
Spectral graph theory (Algebraic graph theory) is the study of spectral properties of matrices associated to graphs. The spectral properties include the study of characteristic polynomial, eigenvalues and eigenvectors of matrices associated to graphs. This also includes the graphs associated to algebraic structures like groups, rings and vector spaces. The major source of research in spectral graph theory has been the study of relationship between the structural and spectral properties of graphs. Another source has research in mathematical chemistry (theoretical/quantum chemistry). One of the major problems in spectral graph theory lies in finding the spectrum of matrices associated to graphs completely or in terms of spectrum of simpler matrices associated with the structure of the graph. Another problem which is worth to mention is to characterise the extremal graphs among all the graphs or among a special class of graphs with respect to a given graph, like spectral radius, the second largest eigenvalue, the smallest eigenvalue, the second smallest eigenvalue, the graph energy and multiplicities of the eigenvalues that can be associated with the graph matrix. The main aim is to discuss the principal properties and structure of a graph from its eigenvalues. It has been observed that the eigenvalues of graphs are closely related to all graph parameters, linking one property to another. Spectral graph theory has a wide range of applications to other areas of mathematical science and to other areas of sciences which include Computer Science, Physics, Chemistry, Biology, Statistics, Engineering etc. The study of graph eigen- values has rich connections with many other areas of mathematics. An important development is the interaction between spectral graph theory and differential geometry. There is an interesting connection between spectral Riemannian geometry and spectral graph theory. Graph operations help in partitioning of the embedding space, maximising inter-cluster affinity and minimising inter-cluster proximity. Spectral graph theory plays a major role in deforming the embedding spaces in geometry. Graph spectra helps us in making conclusions that we cannot recognize the shapes of solids by their sounds. Algebraic spectral methods are also useful in studying the groups and the rings in a new light. This new developing field investigates the spectrum of graphs associated with the algebraic structures like groups and rings. The main motive to study these algebraic structures graphically using spectral analysis is to explore several properties of interest.
Laplacian Eigenvectors Of Graphs
DOWNLOAD
Author : Türker Biyikoglu
language : en
Publisher: Springer
Release Date : 2007-07-07
Laplacian Eigenvectors Of Graphs written by Türker Biyikoglu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-07 with Mathematics categories.
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.
Locating Eigenvalues In Graphs
DOWNLOAD
Author : Carlos Hoppen
language : en
Publisher: Springer Nature
Release Date : 2022-09-21
Locating Eigenvalues In Graphs written by Carlos Hoppen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-21 with Mathematics categories.
This book focuses on linear time eigenvalue location algorithms for graphs. This subject relates to spectral graph theory, a field that combines tools and concepts of linear algebra and combinatorics, with applications ranging from image processing and data analysis to molecular descriptors and random walks. It has attracted a lot of attention and has since emerged as an area on its own. Studies in spectral graph theory seek to determine properties of a graph through matrices associated with it. It turns out that eigenvalues and eigenvectors have surprisingly many connections with the structure of a graph. This book approaches this subject under the perspective of eigenvalue location algorithms. These are algorithms that, given a symmetric graph matrix M and a real interval I, return the number of eigenvalues of M that lie in I. Since the algorithms described here are typically very fast, they allow one to quickly approximate the value of any eigenvalue, which is a basic step in most applications of spectral graph theory. Moreover, these algorithms are convenient theoretical tools for proving bounds on eigenvalues and their multiplicities, which was quite useful to solve longstanding open problems in the area. This book brings these algorithms together, revealing how similar they are in spirit, and presents some of their main applications. This work can be of special interest to graduate students and researchers in spectral graph theory, and to any mathematician who wishes to know more about eigenvalues associated with graphs. It can also serve as a compact textbook for short courses on the topic.
Graph Theory Combinatorics And Algorithms
DOWNLOAD
Author : Y. Alavi
language : en
Publisher:
Release Date : 1995
Graph Theory Combinatorics And Algorithms written by Y. Alavi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Algorithms categories.
Spectral Graph Theory
DOWNLOAD
Author : Fan R. K. Chung
language : en
Publisher: American Mathematical Soc.
Release Date :
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 with Mathematics categories.
Beautifully written and elegantly presented, this book is based on 10 lectures given at the CBMS workshop on spectral graph theory in June 1994 at Fresno State University. Chung's well-written exposition can be likened to a conversation with a good teacher - one who not only gives you the facts, but tells you what is really going on, why it is worth doing, and how it is related to familiar ideas in other areas. The monograph is accessible to the nonexpert who is interested in reading about this evolving area of mathematics.
Inequalities For Graph Eigenvalues
DOWNLOAD
Author : Zoran Stanić
language : en
Publisher: Cambridge University Press
Release Date : 2015-07-23
Inequalities For Graph Eigenvalues written by Zoran Stanić 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 2015-07-23 with Mathematics categories.
This book explores the inequalities for eigenvalues of the six matrices associated with graphs. Includes the main results and selected applications.
Graph Embeddings And Laplacian Eigenvalues
DOWNLOAD
Author : Stephen Guattery
language : en
Publisher:
Release Date : 1998
Graph Embeddings And Laplacian Eigenvalues written by Stephen Guattery and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Embeddings (Mathematics) categories.
Abstract: "Graph embeddings are useful in bounding the smallest nontrivial eigenvalues of Laplacian matrices from below. For an n x n Laplacian, these embedding methods can be characterized as follows: The lower bound is based on a clique embedding into the underlying graph of the Laplacian. An embedding can be represented by a matrix [gamma]; the best possible bound based on this embedding is n/[lambda][subscript max]([gamma superscript T gamma]). However, the best bounds produced by embedding techniques are not tight; they can be off by a factor proportional to log2n for some Laplacians. We show that this gap is a result of the representation of the embedding: by including edge directions in the embedding matrix representation [gamma], it is possible to find an embedding such that [gamma superscript T gamma] has eigenvalues that can be put into a one-to-one correspondence with the eigenvalues of the Laplacian. Specifically, if [lambda] is a nonzero eigenvalue of either matrix, then n/[lambda] is an eigenvalue of the other. Simple transformations map the corresponding eigenvectors to each other. The embedding that produces these correspondences has a simple description in electrical terms if the underlying graph of the Laplaciain [sic] is viewed as a resistive circuit. We also show that a similar technique works for star embeddings when the Laplacian has a zero Dirichlet boundary condition, though the related eigenvalues in this case are reciprocals of each other. In the Dirichlet boundary case, the embedding matrix [gamma] can be used to construct the inverse of the Laplacian. Finally, we connect our results with previous techniques for producing bounds, and provide an illustrative example."
Mathematical Foundations Of Computer Science 2006
DOWNLOAD
Author : Rastislav Královic
language : en
Publisher: Springer
Release Date : 2006-08-29
Mathematical Foundations Of Computer Science 2006 written by Rastislav Královic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-29 with Computers categories.
This book constitutes the refereed proceedings of the 31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006. The book presents 62 revised full papers together with the full papers or abstracts of 7 invited talks. All current aspects in theoretical computer science and its mathematical foundations are addressed, from algorithms and data structures, to complexity, automata, semantics, logic, formal specifications, models of computation, concurrency theory, computational geometry and more.
Structures Of Domination In Graphs
DOWNLOAD
Author : Teresa W. Haynes
language : en
Publisher: Springer Nature
Release Date : 2021-05-04
Structures Of Domination In Graphs written by Teresa W. Haynes and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-04 with Mathematics categories.
This volume comprises 17 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results. The book is divided into 3 parts. The first part focuses on several domination-related concepts: broadcast domination, alliances, domatic numbers, dominator colorings, irredundance in graphs, private neighbor concepts, game domination, varieties of Roman domination and spectral graph theory. The second part covers domination in hypergraphs, chessboards, and digraphs and tournaments. The third part focuses on the development of algorithms and complexity of signed, minus and majority domination, power domination, and alliances in graphs. The third part also includes a chapter on self-stabilizing algorithms. Of extra benefit to the reader, the first chapter includes a glossary of commonly used terms. The book is intended to provide a reference for established researchers in the fields of domination and graph theory and graduate students who wish to gain knowledge of the topics covered as well as an overview of the major accomplishments and proof techniques used in the field.
Spectra Of Graphs
DOWNLOAD
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.