Zeta Functions of Graphs: A Stroll through the Garden - Couverture rigide

Terras, Audrey

Couverture rigide

ISBN 10 : 0521113679 ISBN 13 : 9780521113670

Editeur : Cambridge University Press, 2010

Synopsis

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.

A propos du livre

À propos de l'auteur

Audrey Terras is Professor of Mathematics at the University of California, San Diego.

Détails de l'édition

• Éditeur: Cambridge University Press
• Date d'édition: 2010
• Langue: anglais
• ISBN 10: 0521113679
• ISBN 13: 9780521113670
• Reliure: Relié
• Nombre de pages: 252
• Coordonnées du fabricant: non disponible
• Personne responsable: Avery; https://www.avery.fr/; ; chemin des peupliers 27; Dardilly; France