Spectral Graph Theory Book Pdf

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A Brief Introduction to Spectral Graph Theory

Characterizations of Graphs by their Spectra. Distance-Regular and Similar Graphs. Miscellaneous Results from the Theory of Graph Spectra. Applications to Chemistry and Other Branches of Science. Spectra of Infinite Graphs. Appendix: Spectra of Graphs with Seven Vertices.

Bibliographic Index. The purpose of this volume is to review the results in spectral graph theory which have appeared since The problem of characterizing graphs with least eigenvalue -2 was one of the original problems of spectral graph theory.

The techniques used in the investigation of this problem have continued to be useful in other contexts including forbidden subgraph techniques as well as geometric methods involving root systems. In the meantime, the particular problem giving rise to these methods has been solved almost completely. This is indicated in Chapter 1.

The study of various combinatorial objects including distance regular and distance transitive graphs, association schemes, and block designs have made use of eigenvalue techniques, usually as a method to show the nonexistence of objects with certain parameters. The basic method is to construct a graph which contains the structure of the combinatorial object and then to use the properties of the eigenvalues of the graph.

Methods of this type are given in Chapter 2. Several topics have been included in Chapter 3, including the relationships between the spectrum and automorphism group of a graph, the graph isomorphism and the graph reconstruction problem, spectra of random graphs, and the Shannon capacity problem. Some graph polynomials related to the characteristic polynomial are described in Chapter 4.

These include the matching, distance, and permanental polynomials. Applications of the theory of graph spectra to Chemistry and other branches of science are described from a mathematical viewpoint in Chapter 5. The last chapter is devoted to the extension of the theory of graph spectra to infinite graphs.

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spectral graph theory research papers

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition. There are many undergraduate books on graph theory in general, but few of those books highlight the connection of graph theory with other mathematical fields, for example with group theory or linear algebra. The book under review attempts one such approach, emphasizing the link with linear algebra via the adjacency and Laplacian matrices associated to a given graph. Both such matrices are real symmetric and thus have exactly n real eigenvalues, where n is the number of vertices of the graph. The key point of spectral graph theory is to obtain information on the graph from information on the eigenvalues of its adjacency or Laplacian matrix. After a few examples of computations of the eigenvalues of the adjacency matrix of some concrete graphs, the author introduces general methods to compute these eigenvalues for families of graphs, and proves some general results on the spectra of graphs. The author illustrates the power of the spectral approach obtaining some structural properties of a given graph or a family of graphs from properties of the corresponding eigenvalues.

Chung FRK Discrete isoperimetric inequalities. We work hard to protect your security and privacy. To my knowledge this is the only reference dedicated to spectral methods; however, most major books on graph theory have sections on spectral methods. Objectives were to compare the various hard threshold methods for validity retention of biological information , stability, and reliability. The main objective of spectral graph theory is to relate properties of graphs with the eigenvalues and eigenvectors spectral properties of associated matrices. Previous page of related Sponsored Products.


This book is mostly based on lecture notes from the “Spectral Graph Theory” course that I have taught at Yale, with notes from “Graphs and Networks” and.


A Brief Introduction to Spectral Graph Theory

Characterizations of Graphs by their Spectra. Distance-Regular and Similar Graphs. Miscellaneous Results from the Theory of Graph Spectra.

There seem to be scattered notes on the internet, but I don't know about those. Important early work was done by social scientists: sociologists, We assume that the reader is familiar with ideas from linear algebra and assume limited knowledge in graph theory. Spectral Graph Theory. Spectral graph theory studies how the eigenvalues of the adjacency matrix of a graph, which are purely algebraic quantities, relate to combinatorial properties of the graph. The Laplacian and eigenvalues.

Beautifully written and elegantly presented, this book is based on 10 lectures given at the CBMS workshop on spectral graph theory in June 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. Graduate students and research mathematicians interested in graph theory and its relations to combinatorics, geometry, communication theory, computer science, algebra, and other areas of pure and applied mathematics.

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4 Comments

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  2. Isseniha 16.05.2021 at 00:48

    Spectral graph theory starts by associating matrices to graphs — notably, the adjacency matrix and the Laplacian matrix.

  3. Mallory T. 20.05.2021 at 05:52

    Graph spectra have been studied extensively for more than fifty years.

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