## Spectral Graph Theory, Issue 92Beautifully 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. |

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### Contents

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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### Common terms and phrases

absolute constant achieves the log-Sobolev An_i cartesian product Chapter Cheeger constant clique complete graph compute connected graph consider COROLLARY defined degree derive diameter Dirichlet boundary condition Dirichlet eigenvalues discrepancy distance transitive graph edge density edge generating set edge of G eigenfunction example expander graphs explicit constructions fc-regular function f G satisfies graph G harmonic eigenfunction Harnack inequalities heat kernel implies indexed induced subgraph inputs integer irr G isoperimetric dimension Laplacian LEMMA log-Sobolev constant lower bound multiplicity Neumann boundary condition Neumann eigenvalues non-negative 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 routing rt(G Section Sobolev inequalities spectral graph theory spectrum stationary distribution subset of vertices Suppose G symmetrical graphs upper bound vector vertex boundary vertex set vol G vol X vol volG weighted graph

### Popular passages

Page i - Some topics in probability and analysis, 1989 69 Frank D. Grosshans, Gian-Carlo Rota, and Joel A. Stein, Invariant theory and superalgebras, 1987 68 J. William Helton, Joseph A. Ball, Charles R. Johnson, and John N. Palmer, Operator theory, analytic functions, matrices, and electrical engineering, 1987 67 Harald Upmeier, Jordan algebras in analysis, operator theory, and quantum mechanics, 1987 66 G.

Page xi - The authors would like to acknowledge the support of National Science Foundation through Grant No.