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Zeta Functions of Graphs : A Stroll through the Garden

By: Audrey Terras (Author)

Ksh 26,100.00
Format :

Format(s): DRM PDF

ISBN-13: 9781107212688

Publisher: Cambridge University Press

Imprint: Cambridge University Press

Publication Date: November 18th, 2010

Country of Publication: US

Language: English

Physical Edition EAN: 9780521113670

Category: Mathematical foundations , Discrete mathematics , Number theory

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  • Description

  • Author Bio

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.

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