View in EDS PDF Full Text

Zeta Functions of Graphs : A Stroll Through the Garden

Saved in:
Bibliographic Details
Title: Zeta Functions of Graphs : A Stroll Through the Garden
Description: Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound with number-theoretic functions such as Riemann/Dedekind zeta functions. For example, there is a Riemann hypothesis (which may be false) and prime number theorem for graphs. Explicit constructions of graph coverings use Galois theory to generalize Cayley and Schreier graphs. Then non-isomorphic simple graphs with the same zeta are produced, showing you cannot hear the shape of a graph. The spectra of matrices such as the adjacency and edge adjacency matrices of a graph are essential to the plot of this book, which makes connections with quantum chaos and random matrix theory, plus expander/Ramanujan graphs of interest in computer science. Created for beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and exercises, both theoretical and computer-based, are included throughout.
Authors: Audrey Terras
Resource Type: eBook.
Subjects: Graph theory, Functions, Zeta
Categories: MATHEMATICS / Graphic Methods
Database: eBook Collection (EBSCOhost)
FullText Links:
  – Type: ebook-pdf
Text:
  Availability: 0
Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 337707
RelevancyScore: 1038
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1037.72192382813
IllustrationInfo
ImageInfo – Size: thumb
  Target: https://rps2images.ebscohost.com/rpsweb/othumb?id=NL$337707$PDF&s=r
– Size: medium
  Target: https://rps2images.ebscohost.com/rpsweb/othumb?id=NL$337707$PDF&s=d
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Zeta Functions of Graphs : A Stroll Through the Garden
– Name: Abstract
  Label: Description
  Group: Ab
  Data: Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound with number-theoretic functions such as Riemann/Dedekind zeta functions. For example, there is a Riemann hypothesis (which may be false) and prime number theorem for graphs. Explicit constructions of graph coverings use Galois theory to generalize Cayley and Schreier graphs. Then non-isomorphic simple graphs with the same zeta are produced, showing you cannot hear the shape of a graph. The spectra of matrices such as the adjacency and edge adjacency matrices of a graph are essential to the plot of this book, which makes connections with quantum chaos and random matrix theory, plus expander/Ramanujan graphs of interest in computer science. Created for beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and exercises, both theoretical and computer-based, are included throughout.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Audrey+Terras%22">Audrey Terras</searchLink>
– Name: TypePub
  Label: Resource Type
  Group: TypPub
  Data: eBook.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Functions%2C+Zeta%22">Functions, Zeta</searchLink>
– Name: SubjectBISAC
  Label: Categories
  Group: Su
  Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Graphic+Methods%22">MATHEMATICS / Graphic Methods</searchLink>
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=nlebk&AN=337707
RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 511.5
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Graph theory
        Type: general
      – SubjectFull: Functions, Zeta
        Type: general
    Titles:
      – TitleFull: Zeta Functions of Graphs : A Stroll Through the Garden
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Audrey Terras
      – PersonEntity:
          Name:
            NameFull: Audrey Terras
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2011
            – D: 04
              M: 02
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9780521113670
            – Type: isbn-electronic
              Value: 9780511918681
          Numbering:
            – Type: volume
              Value: 00128
          Titles:
            – TitleFull: Zeta Functions of Graphs : A Stroll Through the Garden
              Type: main
ResultId 1