Spectral Graph Theory, Wydanie 92American Mathematical Soc. - 207 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. |
Spis treści
Eigenvalues and the Laplacian of a graph | 1 |
Isoperimetric problems | 23 |
Diameters and eigenvalues | 43 |
Paths flows and routing | 59 |
Eigenvalues and quasirandomness | 73 |
Expanders and explicit constructions | 91 |
Eigenvalues of symmetrical graphs | 113 |
Eigenvalues of subgraphs with boundary conditions | 127 |
Harnack inequalities | 139 |
Heat kernels | 149 |
Sobolev inequalities | 167 |
Advanced techniques for random walks on graphs | 181 |
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Kluczowe wyrazy i wyrażenia
adjacent cartesian product Chapter Cheeger constant clique complete graph compute connected graph consider convex subgraph COROLLARY defined denote diameter Dirichlet eigenvalues disc G discrete edge density edge generating set eigenfunction eigenvalues example expander graphs explicit constructions function f ƒ² graph G harmonic eigenfunction Harnack inequalities heat kernel homogeneous graph Ht(x indexed induced subgraph inputs invariant irr G isoperimetric dimension k-regular Laplacian LEMMA log-Sobolev constant lower bound matrix Neumann boundary condition Neumann eigenvalues number of edges pairs of vertices Paley graph polynomial proof of Theorem properties proved quasi-random Ramanujan graphs random graph random walk regular graph Riemannian manifolds rt(G Section Sobolev inequalities spectral graph theory stationary distribution subset of vertices Suppose G upper bound vector vertex set vol G vol X vol volX weighted graph x)dx ΔΙ λι ΣΣ
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Strona xi - The authors would like to acknowledge the support of National Science Foundation through Grant No.