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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Krebs, Mike. Expander families and Cayley graphs. New York : Oxford University Press, ©2011 (DLC) 2011027928 (OCoLC)707266118 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Mike Krebs; Anthony Shaheen |

ISBN: | 9780199877485 0199877483 9781283427807 128342780X |

OCLC Number: | 773937205 |

Description: | 1 online resource (xxiv, 258 pages) : illustrations |

Contents: | Cover; Contents; Preface; Notations and conventions; Introduction; 1. What is an expander family?; 2. What is a Cayley graph?; 3. A tale of four invariants; 4. Applications of expander families; PART ONE: Basics; 1. Graph eigenvalues and the isoperimetric constant; 1. Basic definitions from graph theory; 2. Cayley graphs; 3. The adjacency operator; 4. Eigenvalues of regular graphs; 5. The Laplacian; 6. The isoperimetric constant; 7. The Rayleigh-Ritz theorem; 8. Powers and products of adjacency matrices; 9. An upper bound on the isoperimetric constant; Notes; Exercises. |

Responsibility: | Mike Krebs and Anthony Shaheen. |

### Abstract:

Expander families enjoy a wide range of applications in mathematics and computer science, and their study is a fascinating one in its own right. Expander Families and Cayley Graphs: A Beginner's Guide provides an introduction to the mathematical theory underlying these objects.
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