The Resource Expander families and Cayley graphs : a beginner's guide, Mike Krebs and Anthony Shaheen

Expander families and Cayley graphs : a beginner's guide, Mike Krebs and Anthony Shaheen

Label
Expander families and Cayley graphs : a beginner's guide
Title
Expander families and Cayley graphs
Title remainder
a beginner's guide
Statement of responsibility
Mike Krebs and Anthony Shaheen
Creator
Contributor
Subject
Language
eng
Summary
  • "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"--
  • "The theory of expander graphs is a rapidly developing topic in mathematics and computer science, with applications to communication networks, error-correcting codes, cryptography, complexity theory, and much more. Expander Families and Cayley Graphs: A Beginner's Guide is a comprehensive introduction to expander graphs, designed to act as a bridge between classroom study and active research in the field of expanders. It equips those with little or no prior knowledge with the skills necessary to both comprehend current research articles and begin their own research. Central to this book are four invariants that measure the quality of a Cayley graph as a communications network-the isoperimetric constant, the second-largest eigenvalue, the diameter, and the Kazhdan constant. The book poses and answers three core questions: How do these invariants relate to one another? How do they relate to subgroups and quotients? What are their optimal values/growth rates? Chapters cover topics such as: · Graph spectra · A Cheeger-Buser-type inequality for regular graphs · Group quotients and graph coverings · Subgroups and Schreier generators · Ramanujan graphs and the Alon-Boppana theorem · The zig-zag product and its relation to semidirect products of groups · Representation theory and eigenvalues of Cayley graphs · Kazhdan constants The only introductory text on this topic suitable for both undergraduate and graduate students, Expander Families and Cayley Graphs requires only one course in linear algebra and one in group theory. No background in graph theory or representation theory is assumed. Examples and practice problems with varying complexity are included, along with detailed notes on research articles that have appeared in the literature. Many chapters end with suggested research topics that are ideal for student projects"--
Assigning source
  • Provided by publisher
  • Provided by publisher
Cataloging source
N$T
Dewey number
511/.5
Illustrations
illustrations
Index
index present
LC call number
QA166.145
LC item number
.K74 2011eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Label
Expander families and Cayley graphs : a beginner's guide, Mike Krebs and Anthony Shaheen
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 247-252) and index
http://library.link/vocab/branchCode
  • net
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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
Control code
ocn773937205
Dimensions
unknown
Extent
1 online resource (xxiv, 258 pages)
File format
unknown
Form of item
online
Isbn
9780199877485
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other physical details
illustrations
Quality assurance targets
not applicable
http://library.link/vocab/recordID
.b36287490
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)773937205
  • ebsco0199877483

Library Locations

    • Deakin University Library - Geelong Waurn Ponds CampusBorrow it
      75 Pigdons Road, Waurn Ponds, Victoria, 3216, AU
      -38.195656 144.304955
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