Zeta Functions of Graphs

A Stroll through the Garden

Nonfiction, Science & Nature, Mathematics, Discrete Mathematics, Number Theory
Cover of the book Zeta Functions of Graphs by Audrey Terras, Cambridge University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Audrey Terras ISBN: 9781139635493
Publisher: Cambridge University Press Publication: November 18, 2010
Imprint: Cambridge University Press Language: English
Author: Audrey Terras
ISBN: 9781139635493
Publisher: Cambridge University Press
Publication: November 18, 2010
Imprint: Cambridge University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Cambridge University Press

Cover of the book Clinical Gynecology by Audrey Terras
Cover of the book Social Theory by Audrey Terras
Cover of the book Edwards' Treatment of Drinking Problems by Audrey Terras
Cover of the book Linear Algebra: Concepts and Methods by Audrey Terras
Cover of the book World War One by Audrey Terras
Cover of the book Vegetation Dynamics by Audrey Terras
Cover of the book The Cambridge Companion to Renaissance Philosophy by Audrey Terras
Cover of the book Thinking about Bribery by Audrey Terras
Cover of the book The Cambridge Companion to the Gospels by Audrey Terras
Cover of the book Byron's War by Audrey Terras
Cover of the book The Invention of Sustainability by Audrey Terras
Cover of the book Affective Communities in World Politics by Audrey Terras
Cover of the book Islamic Schools in Modern Turkey by Audrey Terras
Cover of the book The Seduction Narrative in Britain, 1747–1800 by Audrey Terras
Cover of the book The Severity of God by Audrey Terras
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy