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Thursday, August 6, 2020 | History

7 edition of Expander families and Cayley graphs found in the catalog.

Expander families and Cayley graphs

a beginner"s guide

by Mike Krebs

  • 385 Want to read
  • 21 Currently reading

Published by Oxford University Press in Oxford, New York .
Written in English

    Subjects:
  • Eigenvalues,
  • MATHEMATICS / Graphic Methods,
  • Cayley graphs,
  • Cayley algebras

  • Edition Notes

    Includes bibliographical references and index.

    StatementMike Krebs, Anthony Shaheen
    ContributionsShaheen, Anthony
    Classifications
    LC ClassificationsQA166.145 .K74 2011
    The Physical Object
    Paginationp. cm.
    ID Numbers
    Open LibraryOL25010983M
    ISBN 109780199767113
    LC Control Number2011027928

      You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. 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 central notion in the book .

    I want to learn the field of spectral graph theory. For this I need a book of article which can help from basic to advance level. Expander families and Cayley graphs Mike Krebs and Anthony. A family fG igof d-regular graphs with jG ij!1as i!1is said to be a family of expander graphs, or a family of expanders, if there exists ">0 such that h(G i) "for all i. We say that a family of groups fH igcan be made into a family of expanders if there exists a positive integer dand a symmetric generating set S i H iof size dfor each i, such.

    Theorem Suppose that S Zt 2 contains no non-trivial solutions to the equation s 1 +s 2 = s01+s02 and (Cay(Zt 2;S)) (1)jSj. Then the hypergraph H(Zt 2;S) is an 2 edge-expander and an 2 64 jSj-triple-expander. By the Alon{Roichman theorem [2], a random set S Zt 2 of order Ct, for C a su ciently large constant, will a.a.s. have the required properties with = 1=2. Books and Book Chapters: Joint with Mike Krebs, part of chapter in Handbook of Discrete and Combinatorial Mathematics, 2nd edition, CRC Press, ; Joint with Mike Krebs, Chapter on Expander Graphs in Handbook of Graph Theory, 2nd edition, CRC Press, pgs. , ; Joint with Mike Krebs, Expander Families and Cayley Graphs: A Beginner's Guide, Oxford University .


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Expander families and Cayley graphs by Mike Krebs Download PDF EPUB FB2

If you are looking forward to learn expander families of graphs in general, or even the Cayley graphs of finite groups, this book is a must read. If you are looking forward to go through the arithmetic aspects of the same, you need to keep this text along with the texts like Sarnak and Valette's book on the Ramanujan by:   Expander Families and Cayley Graphs: A Beginner's Guide - Kindle edition by Krebs, Mike, Shaheen, Anthony.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Expander Families and Cayley Graphs: A Beginner's Guide.5/5(2). Expander Families and Cayley Graphs: A Beginner's Guide provides an introduction to the mathematical theory underlying these objects.

The central tion in the book is that of expansion, which roughly means the quality of a graph as a communications network. Expander families enjoy a wide range of applications in mathematics Expander families and Cayley graphs book 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 central notion in the book is that of expansion, which roughly means the quality of a graph as a communications.

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. "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. Definitions. Intuitively, an expander is a finite, undirected multigraph in which every subset of the vertices that is not "too large" has a "large" boundary.

Different formalisations of these notions give rise to different notions of expanders: edge expanders, vertex expanders, and spectral expanders, as defined below. A disconnected graph is not an expander, since the boundary of a connected.

Krebs / Shaheen, Expander Families and Cayley Graphs,Buch, Bücher schnell und portofrei Beachten Sie bitte die aktuellen Informationen unseres Partners DHL zu Liefereinschränkungen im Ausland. Like Cayley graphs, G-graphs are graphs that are constructed from groups.

A method for constructing expander families of G-graphs is presented and is used to construct new expander families of. Expander Families and Cayley Graphs: A Beginner's Guide provides an introduction to the mathematical theory underlying these objects.

The central notion in the book is that of expansion, which roughly means the quality of a graph as a communications network. Cayley graph, one can obtain a sequence of expander Cayley graphs via an iterative process using the zig-zag theorem.

However, unlike the case of unstructured graphs, the restrictions on generators alluded to above for applying the zig-zag product on Cayley graphs, make iterations a highly nontrivial (and illuminating) task.

Get this from a library. Expander families and Cayley graphs: a beginner's guide. [Mike Krebs; Anthony Shaheen] -- "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.

2 1. Expansion in Cayley graphs Expander graphs: basic theory The objective of this text is to present a number of recent constructions of expander graphs, which are a type of sparse but \pseudorandom" graph of importance in computer science, the theory of random walks, geometric group theory, and in number theory.

The subject of expander. collaboration graph joining mathematicians that have a joint paper. Genealogical trees form another example of this type, although the relation \Xis a child of Y" is most naturally considered as an oriented edge.

Expander graphs, the subject of these notes, are certain families of graphs, becoming. Like Cayley graphs, G-graphs are graphs that are constructed from groups.A method for constructing expander families of G-graphs is presented and is used to construct new expander families of irregular technique depends on a relation between some known expander families of Cayley graphs and certain expander families of l other properties of expander families of.

Abstract. We continue the search, carried out in [Sh1], for new sets of generators for families of finite groups (such as S L 2 (F P)), which make the corresponding Cayley graphs an expander the way to our new result, we survey some of the recent results and methods introduced in [Sh1], based on the use of invariant means on the profinite completion of the finite groups.

One common method for forming expander families is the Cay-ley graph construction. It is an open problem to nd necessary and su cient conditions for a sequence of nite groups to admit an expander family as a sequence of Cayley graphs.

The class of Key words and phrases. expander graph, expander family, solvable group, semidirect product. scientists, since expander graphs, the protagonists of our story come up in numerous and often surprising contexts in both elds.

But, perhaps, we should start with a few words about graphs in general. They are, of course, one of the prime objects of study in Discrete Mathematics. However, graphs are among the most ubiquitous models of both. Expander Families and Cayley Graphs: A Beginner\'s Guide provides an introduction to the mathematical theory underlying these objects\"--\/span>\"@ en\/a> ; \u00A0\u00A0\u00A0\n schema:description\/a> \" \"The theory of expander graphs is a rapidly developing topic in mathematics and computer science, with applications to communication networks.

We present new infinite families of expander graphs of vertex degree 4, which is the minimal possible degree for Cayley graph expanders.

Our first family defines a tower of coverings (with covering indices equals 2) and our second family is given as Cayley graphs of finite groups with very short presentations with only 2 generators and 4 relations.

Both families are based on particular finite. what bounds of the diameter’s of families of graphs will make those families to we will see why Abelian groups do not yield expander families of y, we will state Alon-Boppana theorem and will understand the proof,and will show why Ramanujan graphs with regularity greater than three turns out to be expander graphs.Now my questions are as follows: Are all expander regular graphs are Cayley, or there is a special pages 5 and 6 of Lubotzky's book "Discrete groups, expanding graphs, and invariant measures".

$\endgroup$ – Sam Nead There is a general method which you can use for construction non-Cayley expander from an other family of expanders. The.We will start with general de nitions of Graphs and basic de nitions of expander graphs, their properties, their eigenvalues and random walks on them.

We will give various examples, such as Cayley graphs, which are expanders. An expander graph is a sparse graph that has strong connectivity properties, quanti ed using vertex, edge or spectral.