Zeta Functions of Graphs: A Stroll Through the Garden (BOK)

Audrey Terras

599,00 59900
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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.

Produktfakta

Språk Engelsk Engelsk Innbinding Innbundet
Utgitt 2010 Forfatter Audrey Terras
Forlag
CAMBRIDGE UNIVERSITY PRESS
ISBN 9780521113670
Antall sider 252 Dimensjoner 15,2cm x 22,8cm x 1,9cm
Vekt 530 gram Leverandør Bertram Trading Ltd
Emner og form Mathematical foundations, Discrete mathematics

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