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Lectures on Spectral Graph Theory by Fan R. K. Chung
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About this book :-
Lectures on Spectral Graph Theory
Fan R. K. Chung.
Book Detail :-
Title: Lectures on Spectral Graph Theory
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Author(s): Fan R. K. Chung
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Type: PDF
Language: English
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About Author :-
The author Norman L. Biggs was a lecturer at University of Southampton, lecturer then reader at Royal Holloway, University of London, and Professor of Mathematics at the London School of Economics. He has been on the editorial board of a number of journals, including the Journal of Algebraic Combinatorics. He has been a member of the Council of the London Mathematical Society.
He has written 12 books and over 100 papers on mathematical topics, many of them in algebraic combinatorics and its applications. He became Emeritus Professor in 2006 and continue to teach History of Mathematics in Finance and Economics for undergraduates. He is also Vice-President of the British Society for the History of Mathematics.
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Book Contents :-
Lectures on Spectral Graph Theory
Fan R. K. Chung
cover the following topics.
1. Eigenvalues and the Laplacian of a graph
1.1. Introduction
1.2. The Laplacian and eigenvalues
1.3. Basic facts about the spectrum of a graph
1.4. Eigenvalues of weighted graphs
1.5. Eigenvalues and random walks
2. Isoperimetric problems
2.1. History
2.2. The Cheeger constant of a graph
2.3. The edge expansion of a graph
2.4. The vertex expansion of a graph
2.5. A characterization of the Cheeger constant
2.6. Isoperimetric inequalities for cartesian products
3. Diameters and eigenvalues
3.1. The diameter of a graph
3.2. Eigenvalues and distances between two subsets
3.3. Eigenvalues and distances among many subsets
3.4. Eigenvalue upper bounds for manifolds
4. Paths, flows, and routing
4.1. Paths and sets of paths
4.2. Flows and Cheeger constants
4.3. Eigenvalues and routes with small congestion
4.4. Routing in graphs
4.5. Comparison theorems
5. Eigenvalues and quasi-randomness
5.1. Quasi-randomness
5.2. The discrepancy property
5.3. The deviation of a graph
5.4. Quasi-random graphs
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